Statistics Questions and Answers

A researcher administers a treatment to a sample from a population with a mean of u 60 If the treatment is expected to decrease scores then the null hypothesis would state that 60 True False

Samples of n 36 scores are selected from a population If the distribution of sample means has an expected value of HM 30 and a standard error of y 4 what is the mean and the standard deviation for the population 4 30 and 24 u 30 and o 8 40 and o 4 u 150 and o 18

A sample of n 16 scores is selected from a normal population with 30 and o 9 The probability of obtaining a sample mean greater than 26 is equal to the probability of obtaining a z score greater than z 1 60 True False

A sample is obtained from a normal population with o 20 If the sample mean has a standard error of 10 points then the sample size is n 4 True False

For a normal population a sample of n 9 scores has a standard error of 10 For the same population a sample of n 25 scores would have a standard error of M 10 0 4 6 M 9 M 5

Consider a normal population with u 50 and o 6 A sample size of at least which size needs to be obtained in order to achieve a standard error of oy 2 or less On 16 n 9 O On 3 n 4

7 3 Section Ex A population has mean 25 and standard deviation o 3 Find and o for samples of size n 25 Round your answers to on x decimal place if needed PI

The data to the right represent the number of chocolate chips per cookie in a random sample of a name brand and a store brand Complete parts a to c below S FRE 10 20 30 40 S 10 20 30 40 b Does there appear to be a difference in the number of chips per cookie A Yes The store brand appears to have more chips per cookie OB Yes The name brand appears to have more chips per cookie OC No There appears to be no difference in the number of chips per cookie in conclusion 10 S 20 30 40 Name Brand 24 29 32 Full data set Store Brand 16 18 31 32 28 22 25 25 33 24 26 26 28 35 27 21 28 22 23 31 20 23 20 23 15

Find the value of Za 0 15 The value of Z0 15 is Round to two decimal places as needed

A certain stimulus administered to each of the 12 patients resulted in the following increase of blood pressure 5 2 8 1 3 0 2 1 5 0 4 and 8 Can it be concluded that the stimulus will in general be accompanied by an increase in blood pressure Given for 11 d f toos 2 2 0 05 Solution Here the increments in blood pressure is denoted by d Total 1 1 d 5 2 8 d 25 4 64 mple size n 12 30 3 9 0 2 0 4 6 0 4 1 25 0 16 36 31 185

the random variable X is normally distributed with mean 49 and standard deviation o 8 Compute the probability Be sure to draw a normal curve with the area corresponding to the probability shaded P X 46 Which of the following shaded regions corresponds to P X 46 S OA 46 49 X G P X 46 Round to four decimal places as needed OB 46 49 P o 46 49

Fill in the blanks to complete the following statements a For the shape of the distribution of the sample proportion to be approximately normal it is required that np 1 p 2 b Suppose the proportion of a population that has a certain characteristic is 0 65 The mean of the sampling distribution of p from this population is P This is a reading assessment question Be certain of your answer because you only get one attempt on this question 2 a For the shape of the distribution of the sample proportion to be approximately normal it is required that np 1 P Type an integer or a decimal

Points 0 63 of 1 In the following probability distribution the random variable x represents the number of activities a parent of a 6th to 8th grade student is involved in Complete parts a through f below 3 X 0 1 P X 0294 0207 0 325 0 101 4 0 073 c Compute and interpret the mean of the random variable x The mean is 1 452 activities Type an integer or a decimal Do not round Which of the following interpretations of the mean is correct C OA The observed value of an experiment will be equal to the mean of the random variable in most experiments OB As the number of experiments decreases the mean of the observations will approach the mean of the random variable C The observed value of an experiment will be less than the mean of the random variable in most experiments D As the number of experiments increases the mean of the observations will approach the mean of the random variable d Compute the standard deviation of the random variable x The standard deviation is activities Round to one decimal place as needed S

The random number generator on calculators randomly generates a number between 0 and 1 The random variable X the number generated follows a uniform probability distribution a Identify the graph of the uniform density function b What is the probability of generating a number between 0 37 and 0 72 c What is the probability of generating a number greater than 0 82 ADensity 1 24 14 0 84 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8 1 1 2 a ON b The probability is 0 35 Simplify your answer c The probability is Simplify your answer B 1 24 1 0 8 0 6 0 4 0 24 Density 0 0 0 2 0 4 0 6 0 8 1 1 2 OC A Density 6 0 8 0 6 0 0 2 0 4 0 6 0 8 1 12 1 2 0 4 0 2 Q

Points 0 5 of 1 In the following probability distribution the random variable x represents the number of activities a parent of a 6th to 8th grade student is involved in Complete parts a through f below 0 1 3 0 294 0 207 0 101 X P x 2 0 325 4 0 073 0 1 2 3 4 c Compute and interpret the mean of the random variable x The mean is 1 452 activities Type an integer or a decimal Do not round Which of the following interpretations of the mean is correct C 0 1 2 3 4 www 2 3 4 OA The observed value of an experiment will be equal to the mean of the random variable in most experiments OB As the number of experiments decreases the mean of the observations will approach the mean of the random variable C The observed value of an experiment will be less than the mean of the random variable in most experiments D As the number of experiments increases the mean of the observations will approach the mean of the random variable d Compute the standard deviation of the random variable x The standard deviation is activities Round to one decimal place as needed

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season X 0 1 2 3 4 5 S P x 0 1674 0 3428 0 2908 0 1497 0 0379 0 0114 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment 25 games The number of hits was recorded Approximate the mean and standard deviation of the random var X based on the simulation The simulation was repeated by performing 50 repetitions of the experiment Approximate the mean and standard deviation of the random variable Compare your results to the theoretical mean ar standard deviation What property is being illustrated Click the icon to view the data tables Compute the theoretical mean of the random variable X for the given probability distribution Hx 1 582 hits Round to three decimal places as needed Compute the theoretical standard deviation of the random variable X for the given probability distribution x 1 114 hits Round to three decimal places as needed Approximate the mean of the random variable X based on the simulation for 25 games Xhits Round to three decimal places as needed CIC Data Tables Table of the numbers of hits for 25 games C 3 1 4 10 1 1 3 5 0 1142 3 2 1 2 3 1 0 1 12 1 Table of the numbers of hits for 50 games 9 3 1 4 1 0 1 1 3 50 1 1 4 2 3 2 1 23 1 01 2 2 2 1 12102301 1 1 1 2 0 1 0 3 2 2 2 2003 1 X

nying data represent the ideal number of children for a random sample of 900 adults Complete parts a through d below Click the icon to view the data about ideal numbers of children NUITIVE VER c Compute and interpret the mean of the random variable X The mean is children Round to one decimal place as needed Which of the following interpretations of the mean is correct HUTUS VIH The standard deviation is children Round to one decimal place as needed HUNDE UND OA If many adults were surveyed one would expect the mean ideal number of children to be the mean of the random variable OB The observed ideal number of children will be equal to the mean ideal number of children for most adults OC The observed ideal number of children will be less than the mean ideal number of children for most adults OD If any number of adults were surveyed one would expect the mean ideal number of children to be the mean of the random variable d Compute the standard deviation of the random variable X Ideal Number of Children Data x of children Frequency 9 30 520 254 67 16 4 0 1 2 3 4 5 6 Print Done X

In a recent poll a random sample of adults in some country 18 years and older was asked When you see an ad emphasizing that a product is Made in our country are you more likely to buy it less likely to buy it or neither more nor less likely to buy it The results of the survey by age group are presented in the following contingency table Complete parts a through c Purchase likelihood 18 34 35 44 45 54 55 Total O More likely 1379 74 Less likely 201 378 395 405 24 6 28 16 211 176 111 595 599 532 Neither more nor less likely 281 Total 506 779 2232 a What is the probability that a randomly selected individual is at least 55 years of age given the individual is less likely to buy a product emphasized as Made in our country The probability is approximately Round to three decimal places as needed b What is the probability that a randomly selected individual is less likely to buy a product emphasized as Made in our country given the individual is at least 55 years of age The probability is approximately Round to three decimal places as needed c Are 18 to 34 year olds more likely to buy a product emphasized as Made in our country than individuals in general OYes more likely O No less likely Maxt

16 26 17 17 17 27 18 28 18 28 27 27 19 33 19 36 19 48 20 49 20 20 21 21 22 22 22 22 24 Class Limits

Data AGes 16 22 49 17 22 17 24 17 24 17 24 18 25 25 18 19 26 19 26 19 27 20 27 20 27 20 28 1 28 133 2 BC mean 24 32 Median 22 Mode 22 1 Which measure is the best representation of the age of a typical Student in our Class P why

Scatter Plot Here How many texts did you receive in the last 24 hours vs How many texts did you send in the last 24 hours How many texts did you receive in t How many texts did you receive in the last 24 hours 400 300 200 100 M 1 71 x 9 33 R 0 761 50 100 150

58 A barber measures hair lengths for a random sample of 100 of his customers and gathers data on the growth rates of their hair The data are plotted in the histogram below 0 96 104 1 12 1 20 1 28 1 36 Growth rate cm month Which of the values below is closest to the standard deviation of the 100 values A 0 008 B 0 01 C 0 03 D 0 08 F 1 16

D Consider the three distributions below 10 12 14 16 18 20 3 6 9 12 15 17 Distribution L Distribution M Order the distributions from least to greatest in terms of the proportion of data less than the mean A M L N B N L M C M N L 12 16 20 24 28 32 Distribution N D N M L E L N M

A university conducted a survey of 401 undergraduate students regarding satisfaction with student government Results of the survey are shown in the table by class rank Complete parts a through d below Click the icon to view the table a If a survey participant is selected at random what is the probability that he or she is satisfied with student government P satisfied 0 571 Round to three decimal places as needed b If a survey participant is selected at random what is the probability that he or she is a junior P junior 0 242 D Round to three decimal places as needed c If a survey participant is selected at random what is the probability that he or she is satisfied and a junior P satisfied and junior Round to three decimal places as needed d If a survey participant is selected at random what is the probability that he or she is satisfied or a junior Pisatisfied or junior Round to three decimal places as needed CREED N Data table Satisfied Neutral Not satisfied Total Freshman 53 29 19 101 0 4 Sophomore J nior Senior 51 62 63 19 Print 25 95 17 18 97 Done 15 30 108 Total 229 80 92 401

4 Summary statistics for the number of campsites at public parks in a large western state are as follows Standard Minimum Q Median Q3 Maximum Mean Deviation 58 0 35 61 95 300 A IQR 60 and SD 58 B IQR 60 and SD 63 C IQR 65 and SD 58 D IQR 65 and SD 63 E IQR 62 5 and SD 60 52014 73 2 A check of the data shows that 5 had been subtracted from every value to bring the minimum to 0 for some calculation purpose If 5 is added back to every value what will now be the interquartile range and the standard deviation

B The student scored 2 8 points lower than the class average on the final C The student scored 2 8 standard deviations lower on the final than on the midterm D The student scored 2 8 standard deviations lower on the final than the class average on the midterm exam E The student scored 2 8 standard deviations lower on the final than the class average on the final exam 70 80 90 A 100 110 70 80 90 B 100 110 24 Given the two histograms above which of the following statements is incorrect A As long as the sample sizes are at least 30 the empirical rule applies to both sets B Both sets have roughly the same ranges C The standard deviation of set A is greater than 5 D The standard deviation of set B is greater than 5 E A lower percentage of the values in set A are at least 10 units from its mean than is the case for set B

Stem Leaf 214 28 31334 3556779 401 46 Using the data set above determine if there are any outliers If there are no outliers enter

A study of phone e mail and texting communication in three time periods results in the following segmented bar chart 100 80 60 40 20 2010 2014 2018 Which of the following is greatest is close A The number of texts and e mails in 2010 B The number of e mails in 2014 Texts E mails Phone calls C The number of texts in 2018 D The above are all equal E It is impossible to answer this question without knowing the actual numbers of individual communications involved

3 Counts of the numbers of spam messages received by a company s executives during one week are summarized below Values Under Q 7 9 10 D 4 E 6 Q Median Q3 15 5 20 How many outliers are there A 0 B 1 C 2 21 5 Values Over Q3 28 30 31

36 If a distribution is perfectly symmetric which of must be true A The distribution is uniform B The mean and median are equal C The interquartile range is equal to twice the standard deviation D The range is twice the interquartile range E The range is equal to six times the standard deviation M 25 25 25 25 35 40 19 tiles Q 30 57

Find the following for the data shown 4 25 32 41 47 62 64 71 73 94 What is the percentile of the data value 71 Round to the nearest whole number Which data value represents the 20th percentile

If all the possible random samples with n 81 scores are selected from a normal population with 80 and 0 9 and the mean is calculated for each sample what is the average of all the sample means 81 80 This cannot be determined with the provided information

26 A random sample of scores at a bowling alley one day gives the following summary statistics n 26 x 132 34 s 10 18 min 113 Q 126 med 134 5 Q3 139 and max 160 How many outliers are there A 0 B 1 C 2 D At least 1 E At least 2

51 The prices at which a particular AP Statistics review book are sold at 92 online sites are summarized in the table below Price 12 25 12 50 12 75 13 00 13 50 14 00 15 00 16 00 19 00 5 11 Frequency 24 21 13 10 2 5 1 Which of the following best describes the distribution of prices A Roughly normal B Skewed left C Skewed right D Skewed both left and right E Bimodal

Calculate the 35th percentile of the data shown X 2 9 15 4 17 1 19 4 24 2 27 3 28 6 30

8 9 10 11 12 13 14 15 16 17 18 19 20 data a Based on the boxplot above what is the value for the Q3

6 7 8 9 10 11 12 13 14 15 16 17 18 data Q Based on the boxplot above identify the 5 number summary

Find the following for the data shown 2 8 51 56 72 87 95 7 37 52 66 76 91 What is the percentile of the data value 66 Round to the nearest whole number Which data value represents the 20th percentile

A researcher administers a treatment to a sample of participants selected from a population with 90 If a hypothesis test is used to evaluate the effect of the treatment which combination of factors is most likely to result in rejecting the null hypothesis O a sample mean near 80 with a 05 a sample mean near 80 with a 01 a sample mean much different than 80 with a 05 a sample mean much different than 80 with a 01

A sample from a normal population with u 50 and a 6 has a mean of M 48 20 If this specific sample mean corresponds to a z 1 50 then how many scores are in this particular sample O n 36 n 25 16 n n 9

If a researcher decides to reject the null hypothesis using an alpha level of a 05 at the conclusion of a hypothesis test then they would include the statement of p 05 when writing their research report True False

A sample of n 25 scores is selected from a normal population with a mean of u 80 However the calculated mean for this sample of scores is M 81 not the population mean of u 80 This is consistent with the concept of sampling error True False

A sample of n 100 scores is selected from a normal population with u 60 and o 20 It is very unlikely that the sample mean will be greater than M 66 True False

Childhood participation in sports cultural groups and youth groups appears to be related to improved self esteem for adolescents McGee Williams Howden Chapman Martin Kawachi 2006 In a representative study a sample of n 100 adolescents with a history of group participation is given a standardized self esteem questionnaire For the general population of adolescents scores on this questionnaire form a normal distribution with a mean of u 50 and a standard deviation of o 15 The sample of group participation adolescents had an average of M 53 8 a Does this sample provide enough evidence to conclude that self esteem scores for these adolescents are significantly different from those of the general population Use a two tailed test with a 05 Show all four steps part of the steps have already been given fill in the blanks or make your own changes 50 H Step 1 Ho u Step 2 a Step 3 Participation Participation p Z Step 4 Reject Accept the null hypothesis 50 b Compute Cohen s d to measure the size of the difference Is the effect size small medium or big according to the range mentioned in the lecture Cohen 1988 Show your work

On average a sample of n 36 scores from a normal population with d 10 will provide a better estimate of the population mean than a researcher would get with a sample of n 9 scores from a normal population with d 10 True False

100 Childhood participation in sports cultural groups and youth groups appears to be related to improved self esteem for adolescents McGee Williams Howden Chapman Martin Kawachi 2006 In a representative study a sample of n adolescents with a history of group participation is given a standardized self esteem questionnaire For the general population of adolescents scores on this questionnaire form a normal distribution with a mean of u 50 and a standard deviation of o 15 The sample of group participation adolescents had an average of M 53 8 a Does this sample provide enough evidence to conclude that self esteem scores for these adolescents are significantly different from those of the general population Use a two tailed test with a 05 Show all four steps part of the steps have already been given fill in the blanks or make your own changes 50 H Step 1 Ho Step 2 a Step 3 Participation Participation p Z Step 4 Reject Accept the null hypothesis 50 b Compute Cohen s d to measure the size of the difference Is the effect size small medium or big according to the range mentioned in the lecture Cohen 1988 Show your work

From the table of values below create a histogram and decide whether the data is right left or zero symmetrical skewed GPA Frequency 0 0 5 3 0 6 1 0 7 1 1 1 5 14 1 6 2 0 32 2 1 2 5 51 2 6 3 0 3 0 3 5 3 6 4 0 4 1 4 5 Select one 29 16 6 2 a Zero Skewed Symmetrical Ob Right Skewed d Left Skewed

statements is incorrect A 1 1 35 6 4 3 36 11 B 72 373 46 952138 2 7 7 10 39 1259 6 40 0 17 41 6 41 6 means 416 A The distributions have the same mean B The distributions have the same interquartile range C The distributions have the same range D The distributions have the same standard deviation

Use sigma notation to write the sum 1 1 6 1 6 2 IM 1 1 6 3 1 6 15

results by gender are given in the dotplots below 110 712 414 0 1 2 3 4 5 6 0 1 2 3 4 T Female C The ranges are both 6 D The standard deviations T 56 Male Which of the following is a true statement A One distribution is roughly symmetric the other is skewed right B The difference in their means is less than the difference in their medians are roughly the same of results is equal to the sum of the