Statistics Questions

Several years ago the mean height of women 20 years of age or older was 63 7 inches Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 63 9 inches a State the appropriate null and alternative hypotheses to assess whether women are taller today b Suppose the P value for this test is 0 03 Explain what this value represents c Write a conclusion for this hypothesis test assuming an x 0 10 level of significance CALLY mean marginis 03 7 RIGHTS B There is a 0 03 probability of obtaining a sample mean height of 63 7 inches or taller from a population whose mean height is 63 9 inches OC There is a 0 03 probability of obtaining a sample mean height of exactly 63 9 inches from a population whose mean height is 63 7 inches D There is a 0 03 probability of obtaining a sample mean height of 63 9 inches or shorter from a population whose mean height is 63 7 inches c Write a conclusion for this hypothesis test assuming an x 0 10 level of significance O A Reject the null hypothesis There is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today OB Reject the null hypothesis There is sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today O C Do not reject the null hypothesis There is sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today OD Do not reject the null hypothesis There is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today

We consider the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey The mean and standard deviation of the differences Xread write 0 543 and 8 878 points a Calculate a 95 confidence interval for the average difference between the reading and writing scores of all students Round your answers to two decimal places 1 77 0 69 b Interpret this interval in context Round your answers to two decimal places We are 95 confident that on the reading test students score on average points lower to 0 7 c Does the confidence interval provide convincing evidence that there is a real difference in the average scores Explain Since 0 is included in the interval the confidence interval does not points higher than they do on the writing test provide convincing evidence that there is a real difference in the average scores

The last four years of returns for a stock are as follows Year 1 3 5 Year 2 a What is the average annual return The average return is 28 4 Year 3 12 4 b What is the variance of the stock s returns The variance of the returns is Note Notice that the average return and standard deviation must be entered in percentage format The variance must be entered in decimal format Year 4 3 5 Round to two decimal places c What is the standard deviation of the stock s returns The standard deviation is Round to five decimal places Round to two decimal places

To test Ho H 107 versus H 107 a simple random sample of size n 35 is obtained Complete parts a through e below Click here to view the t Distribution Area in Right Tail OA Yes because the sample is random B No because n 30 OC No because the test is two tailed OD Yes because n 30 b If x 104 0 and s 5 7 compute the test statistic The test statistic is to 3 11 Round to two decimal places as needed c Draw a t distribution with the area that represents the P value shaded Choose the correct graph below OA Q P OB Q 2 O C Q

Calculate the 95 confidence intervals for the four different investments included in the following table Average Return Standard Deviation of returns Small Stocks 20 42 41 46 S P 500 12 07 19 63 The 95 confidence interval of small stocks is between Corporate Bonds 5 72 6 23 and T Bills 4 58 3 81

Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls In 1990 the concentration of calcium in precipitation in a certain area was 0 15 milligrams per liter mg L A random sample of 10 precipitation dates in 2007 results in the following data table Complete parts a through c below Click the icon to view the data table CIDB a State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990 Ho Y 0 15 mg L H V 0 15 mg L

One year the mean age of an inmate on death row was 38 3 years A sociologist wondered whether the mean age of a death row inmate has changed since then She randomly selects 32 death row inmates and finds that their mean age is 36 8 with a standard deviation of 8 5 Construct a 95 confidence interval about the mean age What does the interval imply Click the icon to view the table of critical t values Choose the correct hypotheses Ho H Type integers or decimals Do not round

Explain the difference between statistical significance and practical significance Choose the correct answer below A Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis Practical significance refers to whether the difference between th sample statistic and the parameter stated in the null hypothesis is large enough to be considered important an application OB Statistical significance means that the hypothesis test being performed is useful for building theoretical foundations for other statistical work Practical significance means that the particular application of the hypothesis test is of great importance to the real world OC Statistical significance refers to the type of hypothesis test needed to analyze a population with some tests being more important than Z tests Practical significance refers to how difficult a desired hypothesis test is to perform in an application with some tests being easier to perform than others O D Statistical significance refers to how an unusual event is unlikely to actually appear in a real world application such as every entry in a sample of size 50 having the same value Practical significance refers to how an unusual event is likely to actually appear in a real world application such as a rejection of a null hypothesis using data that looks feasible

Police recorded the average speed of cars driving on a busy street by a school For a sample of 36 speeds it was determined that the average amount over the speed limit for the 36 speeds w 12 6 mph with a standard deviation of 9 mph The 95 confidence interval estimate for this sample is 9 55 mph to 15 65 mph a What is the margin of error for this problem b What size sample is needed to reduce the margin of error to no more than 2

8 Consider any regular pyramid Indicate which line segmen has the greater length a slant height or altitude b lateral edge or radius of the base

The total number of thousands of tons of coal produced per year over a 10 year period for a certain region is provided in the accompanying dataset Use double exponential smoothing to determine which pairs values for a and minimize MAD for this dataset a 0 2 p 0 9 a 0 4 p 0 3 x 1 p 0 6 Click the icon to view the coal production data First find the MAD for each pair of values a and B Type integers or decimals rounded to two decimal places as needed a B 0 9 0 3 0 6 0 2 0 4 1 MAD 53126 00 Coal Production Year 1 2 3 4 5 6 7 8 9 10 Coal Production thousands of tons 434 327 420 421 439 046 477 194 504 178 526 952 546 818 564 876 556 707 570 976 O X

8 Every year the value of a car decreases The following graph illustrates the depreciation over time a What is the initial value of the car 1 mark b How long does it take for the car to lose half of its value 1 mark Value of Car 1000s 26 4228 20 18 16 14 12 10 8 6 4 2 Depreciation of a Car 1 2 3 4 5 6 7 8 9 10 Time in years c Calculate the percentage decrease from the time the car was purchased to 5 years later 2 marks

a survey 42 of the respondents stated that they talk to their pets on the telephone A veterinarian believed this result be too high so he randomly selected 190 pet owners and discovered that 76 of them spoke to their pet on the ephone Does the veterinarian have a right to be skeptical Use the x 0 05 level of significance ick here to view the standard normal distribution table page 1 ick here to view the standard normal distribution table page 2 0 56 Round to two decimal places as needed etermine the critical value s Select the correct choice below and fill in the answer box to complete your choice Round to two decimal places as needed YA Za 1 64 B Za 2 Does the veterinarian have a right to be skeptical A The veterinarian does not have a right to be skeptical There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 42 B The veterinarian has a right to be skeptical There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 42 OC The veterinarian has a right to be skeptical There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is not 42 OD The veterinarian does not have a right to be skeptical There is not sufficient evidence to conclude that the true ON

Several years ago 47 of parents who had children in grades K 12 were satisfied with the quality of education the students receive A recent poll asked 1 065 parents who have children in grades K 12 if they were satisfied with the quality of education the students receive Of the 1 065 surveyed 487 indicated that they were satisfied Construct a 95 confidence interval to assess whether this represents evidence that parents attitudes toward the quality of education have changed Ho P 0 47 versus H p 0 47 Round to two decimal places as needed Use technology to find the 95 confidence interval The lower bound is 0 43 The upper bound is 0 49 Round to two decimal places as needed What is the correct conclusion OA Since the interval does not contain the proportion stated in the null hypothesis there is sufficient evidence that parents attitudes toward the quality of education have changed OB Since the interval contains the proportion stated in the null hypothesis there is sufficient evidence that parents attitudes toward the quality of education have changed OC Since the interval contains the proportion stated in the null hypothesis there is insufficient evidence that parents attitudes toward the quality of education have changed OD Since the interval does not contain the proportion stated in the null hypothesis there is insufficient evidence

Twenty years ago 48 of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science A recent survey found that 302 of 900 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science Do parents feel differently today than they did twenty years ago Use the a 0 05 level of significance Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 Because npo 1 Po 224 6 10 the sample size is less than 5 of the population size and the sample can be reasonably assumed to be random the requirements for testing the hypothesis are satisfied Round to one decimal place as needed What are the null and alternative hypotheses Ho P Type integers or decimals Do not round Determine the test statistic Zo 0 48 versus H p 0 48 Zo 8 67 Round to two decimal places as needed Determine the critical value s Select the correct choice below and fill in the answer box to complete your choice Round to two decimal places as needed OA 2a 2 B Z

Suppose a researcher is testing the hypothesis Ho p 0 3 versus H p 0 3 and she finds the P value to be 0 34 Explain what this means Would she reject the null hypothesis Why Choose the correct explanation below OA If the P value for a particular test statistic is 0 34 she expects results no more extreme than the test statistic in exactly 34 of 100 samples if the null hypothesis is true OB If the P value for a particular test statistic is 0 34 she expects results at least as extreme as the test statistic in exactly 34 of 100 samples if the null hypothesis is true OC If the P value for a particular test statistic is 0 34 she expects results at least as extreme as the test statistic in about 34 of 100 samples if the null hypothesis is true OD If the P value for a particular test statistic is 0 34 she expects results no more extreme than the test statistic in about 34 of 100 samples if the null hypothesis is true

Explain what statistical significance means Choose the correct explanation below OA Statistical significance means that the null hypothesis claims the population proportion is equal to somethi other than 0 5 OB Statistical significance means that the sample standard deviation is unusually small resulting in an unusua large test statistic OC Statistical significance means that the tools used to measure the data introduce error that needs to be accounted for when considering whether or not to reject the null hypothesis O D Statistical significance means that the scenario being analyzed will have a meaningful real world impact OE Statistical significance means that the result observed in a sample is unusual when the null hypothesis is assumed to be true

Test the hypothesis using the P value approach Ho p 0 70 versus H p 0 70 n 150 x 95 0 01 Perform the test using the P value approach P value Round to four decimal places as needed

The headline reporting the results of a poll stated Majority of Adults at Personal Best in the Morning The results indicated that a survey of 1100 adults resulted in 56 stating they were at their personal best in the morning The poll s results were reported with a margin of error of 4 Explain why the poll s headline is accurate Choose the correct answer below OA All the values within the margin of error are greater than 50 O B More than 50 of the respondents answered in the affirmative OC More than 30 people were surveyed

A teacher figures that final grades in the chemistry department are distributed as A 25 B 25 C 40 D 5 F 5 At the end of a randomly selected semester the following number of grades were recorded Calculate the chi square test statistic xa to determine if the grade distribution for the department is different than expected Use 0 01 Grade A B C D F Number 42 36 60 8 14 A 6 87 OB 0 6375 OC 5 25 D 4 82 Y

A random sample of 160 car purchases are selected and categorized by age The results are listed below The age distribution of drivers for the given categories is 18 for the under 26 group 39 for the 26 45 group 31 for the 45 65 group and 12 for the group over 65 Find the critical value xa to test the claim that all ages 2 have purchase rates proportional to their driving rates Use a 0 05 Age Under 26 26 45 46 65 Over 65 Purchases 66 39 25 30 OA 7 815 OB 9 348 OC 11 143 OD 6 251

Find the critical value Determine the critical value for a left tailed test of a population mean at the x 0 025 level of significance based on a sample size of n 18 OA 2 11 OB 3 222 OC 2 101 OD 2 110

When the spinner is spun each color should be selected by the spinner approximately of the time A student suspects that a certain spinner is defective The suspected spinner is spun 90 times The results are shown below Find the P value to test the student s claim Use 0 10 Color Blue Yellow Red Green White Orange Frequency 15 11 17 12 19 16 A P value 0 005 OB 0 025 P value 0 05 OC P value 0 10 D 0 05 P value 0 10

Provide an appropriate response We never conclude Accept Ho in a test of hypothesis This is because A The p value is not small enough B The rejection region is not known OC B p Type Il error is not known OD is the probability of a Type I error

A researcher wishes to estimate the number of households with two computers How large a sample is needed in order to be 99 confident that the sample proportion will not differ from the true proportion by more than 3 A previous study indicates that the proportion of households with two computers is 20 OA 5 OB 966 OC 1179 OD 1474

Provide an appropriate response Determine the expected counts for each outcome n 200 Pi Expected Counts OA Pi O B C OD 0 25 0 20 0 05 0 50 0 25 0 20 Expected Counts 50 40 0 05 0 50 10 100 Pi 0 25 0 20 0 05 0 50 Expected Counts 25 20 5 50 Pi 0 25 0 20 0 05 0 50 Expected Counts 54 38 11 97 Pi 0 25 0 20 0 05 0 50 Expected Counts 500 400 100 1000

Provide an appropriate response If we have a sample of 12 drawn from a normal population then we would use as our test statistic A to with 11 degrees of freedom B zo with 12 degrees of freedom OC to with 12 degrees of freedom D ZO with 11 degrees of freedom

Provide an appropriate response Which of the following is not a characteristic of Students t distribution A For large samples the t and z distributions are nearly equivalent OB symmetric distribution C depends on degrees of freedom D mean of 1

Provide an appropriate response The mean age of professors at a university is greater than 51 2 years If a hypothesis test is performed how should you interpret a decision that rejects the null hypothesis A There is sufficient evidence to support the claim 51 2 OB There is not sufficient evidence to reject the claim 51 2 OC There is sufficient evidence to reject the claim 51 2 D There is not sufficient evidence to support the claim 51 2

The probability of making a Type II error is indicated by the letter OA H Provide an appropriate response OB x OC B D a

Provide an appropriate response Construct a 95 confidence interval for the population mean Assume the population has a normal distribution A sample of 20 part time workers had mean annual earnings of 3120 with a standard deviation of 677 Round to the nearest dollar A 2803 3437 OB 2135 2567 C 1324 1567 OD 2657 2891

Provide an appropriate response The dean of a major university claims that the mean number of hours students study at her University per day is at most 3 8 hours If a hypothesis test is performed how should you interpret a decision that fails to reject the null hypothesis A There is not sufficient evidence to support the claim u 3 8 B There is sufficient evidence to reject the claim 3 8 C There is not sufficient evidence to reject the claim 3 8 D There is sufficient evidence to support the claim 3 8

To select the correct Student s t distribution requires knowing the degrees of freedom How many degrees of freedom are there for a sample of size n OA n 1 B n 1 response OC n OD X H s n

A survey of 400 non fatal accidents showed that 173 involved faulty equipment Find a point estimate for p the population proportion of accidents that involved faulty equipment OA 0 568 OB 0 302 OC 0 433 D 0 762

Provide an appropriate response True or False As the number of degrees of freedom increases the chi square distribution becomes more nearly symmetric OA True OB False

Companying table lists the ages of acting award winners matched by the years in which the awards were won Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables Should we expect that there would be a correlation Use a significance level of a 0 05 Click the icon to view the ages of the award winners Kouna to two decimai piaces as needed The P value is 0 453 Round to three decimal places as needed Because the P value of the linear correlation coefficient is linear correlation between the ages of Best Actresses and Best Actors greater than Should we expect that there would be a correlation I Points 0 73 of 1 13 of 13 points Save the significance level there is not sufficient evidence to support the claim that there is a OA Yes because Best Actors and Best Actresses are typically the same age OB No because Best Actors and Best Actresses are not typically the same age OC Yes because Best Actors and Best Actresses typically appear in the same movies so we should expect the ages to be correlated OD No because Best Actors and Best Actresses typically appear in different movies so we should not expect the

Scores on the quantative portion of an exam have a mean of 589 and a standard deviation of 152 Assume the scores are normally distributed what percentage of students taking the quantive exam score above 6127 Click the icon to view the table of standard scores and percentiles What percentage of students taking the quantitative exam score above 6127 Round to the nearest whole number as needed

The accompanying table shows the wait times minutes from six rides located in three different Walt Disney World theme parks Wait times were reported by Disney and wait times at 10 AM PM were recorded on 50 different days five rows are shown in the accompanying table Use the 10 AM wait times for Space Mountain Rock n Roller Coaster Tower of Terror and Flight of Passage Use a 0 05 significance level to test the claim that the four rides have the same mean wait time at 10 AM Click the icon to view the data table of wait times Determine the null hypothesis Ho H1 H H3 H4 Determine the alternative hypothesis H At least one of the means is different from the others Determine the test statistic The test statistic is Round to two decimal places as needed

According to a report published last year by Pew Research 23 of all American adults lived in a middle class household This year an economist collected data from a random sample of 1460 American adults in order to determine if the percent of American adults who live in a middle class household is higher than 23 State the hypotheses and explain the possible Type 1 and Type 2 errors Determine the null and alternative hypotheses Ho HA A Type I error in the context of this problem would be Select an answer A Type II error in the context of this problem would be Select an answer Rejecting that the percent of all American adults that live in a middle class household is 23 when the percent is really 23 Rejecting that the percent of all American adults that live in a middle class household is 23 when the percent is really lower than that Rejecting that the percent of all American adults that live in a middle class household is 23 when the percent is really higher than that Rejecting that the percent of all American adults that live in a middle class household is 23 when the percent is really different from that Rejecting that the percent of all American adults that live in a middle class household is lower than 23 when the percent is really 23 Rejecting that the percent of all American adults that live in a middle class household is higher than 23 when the percent is really 23 Rejecting that the percent of all American adults that live in a middle class household is different from 23 when the percent is really 23 Failing to reject that the percent of all American adults that live in a middle class household is 23 when the percent is really 23 Failing to reject that the percent of all American adults that live in a middle class household is 23 when the percent is really lower than than Failing to reject that the percent of all American adults that live in a middle class household is 23 when the percent is really higher than tha Failing to reject that the percent of all American adults that live in a middle class household is 23 when the percent is really different from Failing to reject that the percent of all American adults that live in a middle class household is lower than 23 when the percent is really 23 Failing to reject that the percent of all American adults that live in a middle class household is higher than 23 when the percent is really 235 Failing to reject that the percent of all American adulte

A changing electric current in a coil of wire will induce a voltage in a nearby coil Important in the design of transformers the effect is called mutual inductance For two coils the mutual inductance in H as a function of the distance between them is given in the following table Represent the data graphically Distance 0 0 2 0 4 0 6 0 10 0 12 0 cm M ind H 0 78 Choose the correct answer below O A M ind H 0 0 13 Distance cm Q OB M ind H 0 0 13 Distance cm 0 72 0 61 0 47 O C M ind H 0 0 8 0 0 38 13 Distance cm 0 22 0 15 O D M ind H 04 0 13 Distance cm

The sides of a square increase in length at a rate of 4 m sec a At what rate is the area of the square changing when the sides are 15 m long b At what rate is the area of the square changing when the sides are 20 m long a The area of the square is changing at a rate of sides are 15 m long when the

A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ft min What is the rate in the change of area at the instant that the radius is 28 ft Write an equation relating the area of a circle A and the radius of the circle r Type an exact answer using it as needed

part per ppm Listed below mercury ppm found in tuna sushi sampled at different stores in a major city Construct a 95 confidence interval estimate of the mean amount of mercury in the population Does it appear that there i too much mercury in tuna sushi 0 56 0 81 0 10 0 99 1 23 0 52 0 79 AUT SURCO UCuina praves as cucu Does it appear that there is too much mercury in tuna sushi A No because it is possible that the mean is not greater than 1 ppm Also at least one of the sample values is less than 1 ppm so at least some of the fish are safe OB Yes because it is possible that the mean is not greater than 1 ppm Also at least one of the sample values exceeds 1 ppm so at least some of the fish have too much mercury OC Yes because it is possible that the mean is greater than 1 ppm Also at least one of the sample values exceeds 1 ppm so at least some of the fish have too much mercury No because it is not possible that the mean is greater than 1 nom Also at least one of the sample values is less than 1 ppm so at least some of the fish are safe

is shown below Determine whether his calculation was correct or incorrect and then explain why 2 points 1 for the answer 1 for the explanation Points 60 900 15 450 Slope 900 450 450 60 15 45 The Middle of the Hike 10 2 Confirm or disprove Ernest s work by selecting two different points and applying the slope formula Be sure to identify the points you chose 2 points 3 What does the slope tell you about the rate of change in elevation during Ryan s uphill climb What was the total elevation change 2 points 1 for identifying the rate of change 1 for the total elevation change 4 What is the slope of the graph between 120 and 150 minutes What does this

We have people sit in rooms of different colors Red Purple and Green and we test their happiness levels Use the following dataset to determine if the differences between the groups are significant Show all of your work Hint your SSbetween 64 62 and your SSwithin 85 33 a What is the null hypothesis b Conduct the appropriate significance test c Please tell me what the result means in your own words Red 5 10 5 10 10 10 Purple 10 10 20 15 15 5 Green 10 15 5 5 10 10

students was surveyed Their preferences are listed below eBook eBook hard copy eBook eBook eBook eBook hard copy eBook hard copy eBook eBook eBook eBook hard copy eBook eBook eBook eBook hard copy hard copy eBook hard copy eBook eBook hard copy eBook eBook eBook eBook Determine the point estimate p and the sample standard Round the sample proportion to four decimal places and round the standard deviation to six decimal deviation Sp

4 Does the depicted graph seem to indicate evidence of a significant interaction Interaction Plot for Enjoyment Fitted Means Food Condiment Mean of Enjoyment 95 90 85 80 75 70 65 60 Hot Dog Food Ice Cream Condiment Chocolate Sauce Mustard

X 112 2 o Determine the point estimate and the sample standard deviation s for these data Round the solutions to four decimal places if necessary S 127 116 90 115 13 30 or 130 109 110 91 Using a 99 confidence level determine the margin of error E and a 99 confidence interval for the average clutch size of green sea turtles at the Archie Carr National Wildlife Refuge this season Report the confidence interval using interval notation Round solutions to two decimal places if necessary The margin of error is given by E 10 28 X A 99 confidence interval is given by 101 92 122 48

Let the polynomial be ax bx c and its zeroes be and B

the displayed results and use a 0 05 significance level What do you conclude Click the icon to view the data and two way analysis of variance results Fandomly selected U S Army personnel collected as part of a large reputable study Results from two way analysis of variance are also shown Use First test for an interaction between the two factors Determine the null and alternative hypotheses Choose the correct answer below OA Ho Distances between pupils are affected by an interaction between gender and handedness H Distances between pupils are not affected by an interaction between gender and handedness B Ho Distances between pupils are not affected by an interaction between gender and handedness H Distances between pupils are affected by an interaction between gender and handedness OC Ho Distances between pupils are not affected by handedness H Distances between pupils are affected by handedness OD Ho Distances between pupils are not affected by gender H Distances between pupils are affected by gender Determine the test statistic The test statistic is Round to two decimal places as needed Data and Two Way ANOVA Results Source Interaction Female Male DF 1 Row Variable 1 Column Variable 1 SS 24 2 57 8 28 8 Right Handed 65 63 61 60 57 67 62 66 70 69 MS 24 2 57 8 28 8 Left Handed 71 63 62 70 63 69 69 63 68 66 Test Stat F 2 19501 5 24263 2 61224 Critical F 4 49401 4 49401 4 49401 P Value 0 15788 0 03597 0 12559 X