Statistics Questions

The US Department of Energy reported that 45 of homes were heated by natural gas A random sample of 346 homes in Oregon found that 146 were heated by natural gas Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported Use a 5 significance level Give answer to at least 4 decimal places a What are the correct hypotheses Select the correct symbols and use decimal values not percentages Ho Select an answer H Select an answer Based on the hypotheses compute the following b Test Statistic c p value V d Based on the above we choose to Select an answer e The correct summary would be Select an answer that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 45

Part 0 5 Part 1 of 5 2 3 Ho H 4 Is there a doctor in the house A market research firm reported the mean annual earnings of all family practitioners in the United States was 178 258 A random sample of 44 family practitioners in Los Angeles had mean earnings of x 193 250 with a standard deviation of 41 407 Do the data provide sufficient evidence to conclude that the mean salary for family practitioners in Los Angeles differs from the national average Use the a 0 01 level of significance and the P value method with the TI 84 Plus calculator 5 a State the appropriate null and alternate hypotheses This hypothesis test is a Choose one Y test O O 6 X 00 7 0 0 0 co 7 Hel 40 M d

4 College tuition The mean annual tuition and fees for a sample of 13 private colleges in California was 38 000 with a standard deviation of 7900 A dotplot shows that it is reasonable to assume that the population is approximately normal Can you conclude that the mean tuition and fees for private institutions in California differs from 35 000 Use the a 0 01 level of significance and the P value method with the TI 84 Plus calculator Part 0 5 Part 1 of 5 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test OD X O 3

Select the appropriate word or phrase to complete the sentence The number of degrees of freedom for the Student s t test of a population mean is always 1 less than the Choose one sample mean critical value significance level sample size X

A 2011 Gallup survey based on telephone and face to face interviews with 4 220 adults in China aged 15 and older suggests that 30 smoke regularly or occasionally The following is also noted one can say with 95 confidence that the maximum margin of sampling error is 2 1 percentage points Which of the following is true based on the results of this survey OWe are 95 confident that 27 9 to 32 1 of all Chinese adults smoke O Exactly 30 of all Chinese adults smoke Olf we were to randomly sample another group of 4 220 Chinese adults we would find that exactly 30 of them smoke as well We are 95 confident that 25 8 to 34 2 of all Chinese adults smoke If the sample size was larger the margin of error would be larger as well

Part 2 3 Part 3 of 3 Determine whether to reject Ho b Since the test statistic z 2 31 c Since the test statistic z 2 31 Choose one Choose one in the critical region we in the critical region we Choose one Ho at the a 0 05 level Choose one Ho at the a 0 01 level

P value 0 2030 Correct Answer 0 2002 Part 2 4 Part 3 of 4 c Determine whether to reject Ho Use the a 0 01 level of significance Choose one Ho at the a 0 01 level X S

You intend to estimate a population mean from the following sample 6 9 3 1 3 52 6 58 8 4 4 46 9 35 3 39 2 23 4 27 3 49 2 89 6 21 5 47 3 7 5 11 7 26 8 32 8 5 9 41 7 6 5 28 9 25 1 73 7 64 1 65 7 11 10 6 1 2 28 9 31 8 34 9 49 5 16 8 12 70 2 33 8 31 7 31 7 22 6 43 3 45 4 20 77 66 3 35 2 17 1 27 5 58 8 30 2 Find the 90 confidence interval Enter your answer as a tri linear inequality accurate to two decima places because the sample data are reported accurate to one decimal place f

Find the sum of squares error E for the least squares line fit to the four points in the figure Q AY y 11x43 8 6 odu G E Type an integer or a decis

16 The equation that best models the linearized data for a particular data set is logy 0 02396x 48153 a What does the number 0 02396 tell you about the pattern exhibited by the scatterplot of the original data set b Based on the equation what is the value of y whenx 0 Show your work

The world s smallest mammal is the bumblebee bat also known as Kitti s hog nosed bat or Craseonycteris thonglongyai Such bats are roughly the size of a large bumblebee A sample of bats weighed in grams is given below Assume that bat weights are normally distributed Find the 95 confidence interval of the mean Weight 1 57 1 52 1 51 1 98 1 95 2 17 1 65 2 03 1 59 2 18 Do not roun Select an answer

CRO Suppose you are a researcher in a hospital You are experimenting with a new sedative You collect data from a random sample of 13 patients The period of effectiveness of the sedative for each patient in hours is as follows Hours 2 3 2 7 2 7 2 4 2 6 2 5 2 2 4 2 4 2 2 4 3 2 8 a What is a point estimate for the population mea length of time Round answer to 4 decimal places b What must be true in order to construct a confidence interval in this situation Select an answer c Construct a 95 confidence interval for the population mean length of time Enter your answer as an open interval i e parentheses example 5 2314 8 1245 Round upper and lower bounds to 4 decimal places d What does it mean to be 95 confident in this problem 0 95 of all confidence intervals found using this same sampling technique will contain the population mean time O95 of all times will fall within this interval O The confidence interval contains 95 of all sample times O There is a 95 chance that the confidence interval contains the sample mean time e Suppose that the company releases a statement that the mean time for all patients is 2 hours

Trydint bubble gum company claims that 8 out of 10 people prefer their gum to Eklypse Test their claim at the 90 confidence level The null and alternative hypothesis in symbols would be Ho 20 8 H 0 8 Ho p20 8 H p 0 8 Ho p 0 8 H 0 8 Ho p 0 8 H p 0 8 Ho p 0 8 H p 0 8 Ho 0 8 H 0 8 The null hypothesis in words would be The proportion of all people that prefer Trydint gum is less than 0 8 The proportion of people in a sample that prefer Trydint gum is not 0 8 The proportion of all people that prefer Trydint gum is greater than 0 8 The average of people that prefer Trydint gum is 0 8 The average of people that prefer Trydint gum is not 0 8 The proportion of all people that prefer Trydint gum is 0 8 The proportion of people in a sample that prefers Trydint gum is 0 8

A nurse claims the average number of patients per shift is 50 For which confidence interval should you reject Ho 48 to 51 52 to 55 47 to 52 49 to 55

Reject Correct Answer Do not reject Part 3 4 Part 4 of 4 the null hypothesis Ho State a conclusion There Choose one enough evidence to conclude that the mean weight of six year old girls is higher in 2006 2002

In a survey 10 people were asked how much they spent on their child s last birthday gift The results were roughly bell shaped with a mean and standard deviation of 33 and 15 respectively Construct a confidence interval at a 99 confidence level Give your answers to one decimal place Answer should be written in E format H

The pulse rates of 140 randomly selected adult males vary from a low of 45 bpm to a high of 125 bpm Find the minshum sample size required to estimate the mean pulse rate of adult males Assume that we want 98 confidence that the sample mean is within 2 bpm of the population mean a Find the sample size using the range rule of thumb to estimate o n 542 Type a whole number

Shade the intersection of the following system of inequalities y x 1 3 y 2x 4 A graphing utility was used to produce a table of values for functions y and y Determine the intersection of these two functions X Using the table of values from the graphing utility above determine Y 5 Y 3 GB7652 Y 17 15 13 HAHAR75 7534 11 Y2 270 HAHRB76 12 11 Using the table of values from the graphing utility above determine the x value that makes Y 7 Y 7 Y x 11 and Y x 7

b Is Ho rejected at the a 0 05 level c Is Ho rejected at the a 0 01 level Part 1 of 3 a Compute the value of the test statistic Round the answer to at least two decimal places 2 31 z Part 1 3 Part 2 of 3 Choose the correct type of hypothesis test Then find the critical values for a 0 05 and a 0 01 Round your answers to three decimal places necessary H Left tailed Critical Values for a 0 05 Critical Values for a 0 01

Measuring lung function One of the measurements used to determine the health of a person s lungs is the amount of air a person can exhale under force in one second This is called forced expiratory volume in one second and is abbreviated FEV Assume the mean FEV for 10 year old boys is 2 1 liters and that the population standard deviation is a 0 5 A random sample of 100 10 year old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV of 2 09 liters Can you conclude that the mean FEV in the high pollution community differs from 2 1 liters Use the a 0 05 level of significance and the P value method with the TI 84 calculator Part 1 of 4 Question Attempt 1 of 3 State the appropriate null and alternate hypotheses Ho u 2 1 H 2 1 This hypothesis test is a two tailed test Part 1 4 Part 2 of 4 d

Part 2 of 4 Find the P value Round the answer to at least four decimal places P value 0 0258 Part 2 4 Part 3 of 4 Determine whether to reject Ho Choose one Reject Do Not Reject the null hypothesis Ho X

a State the appropriate null and alternate hypotheses b Compute the P value c State a conclusion Use the a 0 01 level of significance Part 1 of 4 a State the appropriate null and alternate hypotheses Ho 20 8 H 20 8 This hypothesis test is a two tailed Part 1 4 Part 2 of 4 test b Compute the P value Round the answer to at least four decimal places

sample of 180 six year old girls weighed between 2003 and 2006 had an average weight of 50 4 pounds Assume the population standard deviation is a 16 5 pounds Can you conclude that the mean weight of six year old girls is higher in 2006 than in 2002 Use the a 0 10 level of significance and the P value method with the TI 84 calculator Part 1 of 4 State the appropriate null and alternate hypotheses Ho 49 3 H 49 3 The hypothesis test is a right tailed Part 1 4 Part 2 of 4 test Compute the P value Round your answer to at least four decimal places Espa o C E 5 d

Lifetimes of AAA batteries are approximately normally distributed A manufacturer wants to estimate the standard deviation of the lifetime of the AAA batteries it produces A random sample of 16 AAA batteries produced by this manufacturer lasted a mean of 11 hours with a standard deviation of 1 8 hours Find a 90 confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer Then give its lower limit and upper limit Carry your intermediate computations to at least three decimal places Round your answers to at least two decimal places If necessary consult a list of formulas Lower limit Upper limit X

What are the degrees of tre d f 4 What is the critical value for this sample Round to four decimal places critical value 13 277 Complete the table by calculating the expected frequencies Observed Expected Category Frequency Frequency A B C D E 14 13 13 5 8 10 6 10 6 Or 10 6 0 10 6 0 10 6 B g

What are the degrees of freedom d f 4 A B C D E What is the critical value for this sample Round to four decimal places critical value 13 277 Complete the table by calculating the expected frequencies Observed Expected Frequency Frequency 14 Category A B C 14 13 13 5 8 13 13

Response A B C D E Observed Frequency 12 23 24 21 9 Expected Frequency 17 8 17 8 17 8 17 8 17 8 Or OT 0 OT O E E 1 8898 1 5191 2 1595 0 5752 4 3505 0 0 OT 03 00 What is the x test statistic for this data Round to four decimal places x Enter an integer or decimal number accurate to at least 3 decimal places more What is the p value Round to four decimal places p value

the a 0 05 significance level test the claim that the responses occur with the same frequency Ho the test question responses occur with the same frequency Ha at least one question response occurs with a different frequency Response A B C D E Observed Expected Frequency Frequency 12 23 24 21 9 0 E E B What is the x test statistic for this data Round to four decimal places x2 What is the n yalue Round to four decimal places Part 2 of

Complete the table by calculating the expected frequencies Expected Frequency Category A B C D E Observed Frequency 14 13 13 5 8 What is the chi square test statistic Round to three decimal places

4 categories occur with the following distribution Category A gives 40 category B gives 30 category C gives 10 and category D gives 20 of the distribution Ho the categories correspond to the given distribution Ha at least one category does not correspond to the given distribution Complete the table by calculating the expected frequencies Category A B C D Observed Expected Frequency Frequency 32 23 13 41 43 6 32 7 10 9 21 8 Or E E 0 0 What is the chi square test statistic for this data Round to three decimal places Part 2 of E

15 An ecologist working with the New Jersey Department of Environmental Projection has been tasked with monitoring the water quality at beaches near Monmouth University She has recruited some of her friends to measure the concentration of Enterococcus faecalis a type of bacterium found in the gastrointestinal tract of humans and other mammals at six total beaches Over the course of several months they collected 13 samples from each beach The local nonprofit funding the research is interested in whether the log concentration of Enterococcus faecalis differs amongst the six beaches To begin the ecologist wants to determine if there is a difference in log concentration between beaches 2 and 4 Use the R printout to answer the following questions a Based on the boxplots does it appear that the log concentration of Enterococcus faecalis at beach 2 is Normally distributed Explain your reasoning according to the boxplot we can see that the log concentratio of the enterococcus facealis at beach 2 is not normally distributed due to the median box being closer to the bottom of b What test could the ecologist use to test for a difference between the two beaches A T test would be optimal in this scenario c What is the test statistic for the test you identified in the previous part How is it computed

e Test the claim that the log concentration of Enterococcus faecalis at beaches 2 and 4 differ at the 0 05 significance level

1 A study randomly assigned adult subjects to one of three exercise treatments 1 a single long exercise period five days per week 2 several ten minute exercise periods five days per week and 3 several ten minute periods five days per week using a home treadmill The study report contains the following summary statistics about weight loss in kilograms after six months of treatment Treatment Long periods Multiple short periods Multiple short periods with treadmill Here is a partial ANOVA table based on these data Source df Group Error The Total Sums of Squares 20 032 Mean 10 2 9 3 10 2 3 In Q1 the mean square for groups MSG is Mean Square 18 456 4 In Q1 what is the value of the F statistic Std Dev n 37 4 2 4 5 5 2 2 In Q1 what is the denominator degrees of freedom for the ANOVA F Ratio What is the numerator degrees of freedom for the ANOVA 112 10 016 0 54 36 62 42 112 5 In Q1 what is the alternative hypothesis for the ANOVA a The population mean weight loss after six months is greatest with multiple short periods of exercise using a treadmill b The population mean weight loss after six months is different for each of the three exercise conditions c The population mean weight loss after six months is not the same for the three exercise conditions d The population mean weight loss after six months is the same for all three exercise conditions

Part 0 4 Part 1 of 4 Measuring lung function One of the measurements used to determine the health of a person s lungs is the amount of air a person can exhale under force in one second This is called forced expiratory volume in one second and is abbreviated FEV Assume the mean FEV for 10 year old boys is 2 1 liters and that the population standard deviation is a 0 5 A random sample of 100 10 year old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV of 2 09 liters Can you conclude that the mean FEV in the high pollution community differs from 2 1 liters Use the a 0 05 level of significance and the P value method with the TI 84 calculator 3 00 State the appropriate null and alternate hypotheses Ho H 5 This hypothesis test is a Choose one test 0 0 O O 0 0 8 Espa ol 8 E

Facebook A study showed that two years ago the mean time spent per visit to Facebook was 20 8 minutes Assume the standard deviation is a 8 0 minutes Suppose that a simple random sample of 105 visits was selected this year and has a sample mean of x 21 8 minutes A social scientist is interested to know whether the mean time of Facebook visits has changed Use the a 0 01 level of significance and the P value method with the TI 84 calculator a State the appropriate null and alternate hypotheses b Compute the P value c State a conclusion Use the a 0 01 level of significance Part 0 4 Part 1 of 4 a State the appropriate null and alternate hypotheses Ho H 0 0 O 0 0 8 E

Heavy children Are children heavier now than they were in the past The National Health and Nutrition Examination Survey NHANES taken between 1999 and 2002 reported that the mean weight of six year old girls in the United States was 49 3 pounds Another NHANES survey published in 2008 reported that a sample of 180 six year old girls weighed between 2003 and 2006 had an average weight of 50 4 pounds Assume the population standard deviation is o 16 5 pounds Can you conclude that the mean weight of six year old girls is higher in 2006 than in 2002 Use the a 0 10 level of significance and the P value method with the TI 84 calculator Part 0 4 Part 1 of 4 State the appropriate null and alternate hypotheses Ho H The hypothesis test is a Choose one test 0 0 0 0 0 0 0 8 C E 13 ola

Part 0 3 Part 1 of 3 Z 4 A test is made of Ho 14 versus H 14 A sample of size n 48 is drawn and x 12 The population standard deviation is a 6 a Compute the value of the test statistic z b Is Ho rejected at the a 0 05 level c Is Ho rejected at the a 0 01 level X 5 S 6 7 a Compute the value of the test statistic Round the answer to at least two decimal places 8 Es

Part 0 4 Part 1 of 4 Calibrating a scale Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology NIST in Washington D C Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams The standard deviation for scale reading is known to be a 2 0 They weigh this weight on the scale 55 times and read the result each time The 55 scale readings have a sample mean of x 1000 6 grams The scale is out of calibration if the mean scale reading differs from 1000 grams The technicians want to perform a hypothesis test to determine whether the scale is out of calibration Use the a 0 10 level of significance and the P value method with the TI 84 calculator State the appropriate null and alternate hypotheses Ho H 6 This hypothesis test is a choose one test 7 O 0 0 0 0 0 8 Mich 8 00 E 200 ola

5 Select the appropriate word or phrase to complete the sentence 6 8 The smaller the P value is the stronger the evidence against the Choose one hypothesis becomes critical null noncritical albant X

Identify the following statements as true or false Part 1 of 4 If P 0 03 the result is statistically significant at the a 0 02 level The statement is Choose one true false Part 2 of 4 X If P 0 03 the null hypothesis is rejected at the a 0 02 level The statement is Choose one Y

13 In a study to investigate the effects of regular exercise on raising high density lipoprotein HDL cholesterol levels good cholesterol a random sample of five male subjects known to have low HDL levels had their HDL measured at the beginning of the study and then again after six months on a regular exercise schedule The data are given in the following table Subject Initial HDL HDL after 6 months Difference 1 31 39 8 c n 8 d n 10 2 36 32 4 3 32 44 12 4 28 34 6 5 37 39 2 The data are to be analyzed using the Wilcoxon signed rank test What is the effective sample size n to be used when calculating the test statistic a n 4 b n 5 14 At The researcher is interested in testing the following one sided test Ho Initial and final HDL measurements have the same distribution H Final HDL levels are systematically lower If the standardized value of Wt is z 1 48 What is the P value for the Wilcoxon signed rank test W a 0 0281 b 0 0329 c 0 0495 d 0 0694

6 In Q1 what is the P value for the ANOVA that tests for equality of the population means of the three treatments P value 0 4173 a Less than 0 01 b Between 0 01 and 0 05 c Between 0 05 and 0 10 d Greater than 0 10

8 An experiment examined the psychophysiological effect of THC the active ingredient in marijuana The study recruited a sample of 18 young adults who were habitual marijuana smokers Subjects came to the lab three times each time completing the same questionnaire but each time smoking a different marijuana cigarette one with 3 9 THC one with 1 8 THC and one with no THC a placebo The order of the conditions was randomized in a double blind design Why can we not use a one way ANOVA procedure here to test whether the mean feeling of high is the same for all three THC amounts a The assumption of independent random samples is not met b The assumption of Normality is not met c The assumption of equal population standard deviations is not met d The explanatory variable is categorical

14 At The researcher is interested in testing the following one sided test Ho Initial and final HDL measurements have the same distribution H Final HDL levels are systematically lower If the standardized value of W is z 1 48 What is the P value for the Wilcoxon signed rank test W a 0 0281 b 0 0329 c 0 0495 d 0 0694

12 If the standardized value of W is z 2 32 The researcher is interested in testing the following two sided test Ho No difference in distribution of scores Ha One of the herbicides produces seedlings that tend to have higher heights Using appropriate technology what is the P value for the test a 0 0102 b 0 0125 c 0 0204 d 0 0250

7 The ANOVA procedure relies on three important assumptions to be valid The data are independent random samples The populations are normally distributed or the sample sizes are large enough The populations have the same standard deviation o

11 Some researchers have suggested that stem pitting disease in peach tree seedlings can be controlled with soil treatment An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides In an experimental field containing 12 seedlings 6 were randomly selected throughout the field to receive Herbicide A The remaining 6 received Herbicide B Soil and weeds for each seedling were treated with the appropriate herbicide for three months at which point the height in centimeters was recorded for each seedling The following results were obtained Herbicide A B Let W the Wilcoxon rank sum test statistic be the sum of the ranks assigned to the heights of peach seedlings receiving Herbicide A a 7 b 8 Height cm 97 93 91 91 89 87 91 87 84 78 74 69 When ranking all the observations which rank should be assigned to the heights of 89 cm C 8 5 d 9

10 Researchers wish to examine the effectiveness of a new weight loss pill A total of 200 obese adults are randomly assigned to one of four conditions weight loss pill alone weight loss pill with a low fat diet placebo pill alone or placebo pill with a low fat diet The weight loss after six months of treatment is recorded in pounds for each subject To analyze these data which inference procedure would you use a z test b t test c ANOVA F test d Chi square test

9 True False Interchanging the degrees of freedom for the F distribution changes the distribution so order of parameters is very important a True b False

The accompanying table shows the maximum weights in kilograms for which one repetition of a half squat can be performed and the times on seconds to run a 10 meter sprvi soccer players Complete parts a through d below Click here to view the data table Click here to view the table of critical values for the Pearson correlation coefficient a Display the data in a scatter plot Choose the correct graph below OA OB DOVERNE MILL 200 100 160 140 14 Max Weight Dig b Calculate the sample correlation coefficient r Round to three decimal places as needed Data Table Maximum weight x 175 100 155 205 150 190 180 160 105 185 156 Time y 1 92 1 09 2 15 1 54 2 19 1 75 1 85 201 1 74 1 78 211 D 244 224 20 14 16 140 Max Wight 220 CITT 00 220 200 106 166 146 14 Mar thank Da n 8 Critical Values for the Pearson Correlation Coefficient 10 11 12 13 14 15 16 17 18 19 20 21 22 0 05 0 950 0 878 0 811 0 754 0 707 0 006 0 632 0 002 0 576 0 553 0 532 0 514 0 497 0 482 0 468 0 456 0444 0433 0 423 0 01 0 990 0 959 0 917 0 875 0 834 0 798 0 765 0 735 0 708 0 084 0 661 0 641 0 623 0 600 0 500 0 575 22 26 16 16 14 140 0 561 0 540 0 537 Max Verst 220 X k answer