Final Examination in Applied Statistical Methods
A grocery store was interested in understanding the level of brand loyalty for different products.
Nielsen Corporation states that brand loyalty to milk is 65%. The grocery store randomly polled
200 customers that had just purchased milk and found that 150 were loyal to one brand of milk.
They would like to know if this shows evidence that customer loyalty to brand of milk has
changed. Which test should be used? - answers✔✔a. Single sample test of means with
unknown variance (standard deviation)
b. Two sample test of means with unknown variance (standard deviation) but assumed equal
c. Two sample test of proportions
d. Single sample test of proportions
d. Single sample test of proportions
Consider the SAT question (problem 4) of the homework that is testing whether or not SAT
scores increased by at least 30 points after going through a program. The two errors that can be
made are to conclude that the program increases by at least 30 points even though they do not
and to conclude that the program fails to increase by at least 30 points even though it does. The
independent agency conducting the test has decided that the error of concluding the program
failed to hit its target when really the company can provide a 30 point increase is substantially
more important. This error would irreparably damage the company's reputation. They would
like to ensure that they do not make this error even if that means increasing the chance that
they falsely conclude the company provides its promised increase in score. When selecting their
alpha (choosing between 0.01, 0.05 and 0.10) which alpha level provides the highest -
answers✔✔a. Alpha = 0.01
b. Alpha = 0.05
c. Alpha = 0.10
, c. Alpha = 0.10
This is a Type II error; decreased as the significance level (alpha) is increased
I have two paired samples of means and should conduct a two sample hypothesis test of paired
means with unknown variance. If I instead conduct a two sample test of independent means
with unknown variance, I am more likely to reject the null hypothesis. - answers✔✔a. True
b. False
a. True
Higher variation and less power
A 20-minute consumer survey that included a $5 Starbucks gift card was emailed to 500 adults
aged 25-34. The survey resulted in 65 responses. The same 20-minute consumer survey was
emailed to 500 adults aged 25-34 without the Starbucks gift card. That survey resulted in 45
responses. We would like to know if the inclusion of a Starbucks gift card led to an increase in
survey response rate. Which of the following hypotheses should be used? (Assume that sample
1 is with the gift card and sample 2 is without the gift card). - answers✔✔a. H0: π1-π2=0; H1:
π1-π2≠0
b. H0: π1-π2≤0; H1: π1-π2>0
c. H0: μ1- μ2=0; H1: H0: μ1- μ2≠0
d. H0: μ1- μ2≥0; H1: H0: μ1- μ2<0
b. H0: π1-π2≤0; H1: π1-π2>0
A company has conducted a statistical two sample hypothesis test of means with known
variances with one tail. The critical value they used was +2.326 (alpha of 0.01). The test statistic
they calculated was 1.655 (pvalue of 0.049). Based on this, they decided to fail to reject the null
hypothesis. What can you say about their sensitivity to their choice of alpha? - answers✔✔a. If
they had selected a larger alpha (0.05 or 0.10), they would have rejected
b. If they had selected a larger alpha (0.05 or 0.10), they would have failed to reject
A grocery store was interested in understanding the level of brand loyalty for different products.
Nielsen Corporation states that brand loyalty to milk is 65%. The grocery store randomly polled
200 customers that had just purchased milk and found that 150 were loyal to one brand of milk.
They would like to know if this shows evidence that customer loyalty to brand of milk has
changed. Which test should be used? - answers✔✔a. Single sample test of means with
unknown variance (standard deviation)
b. Two sample test of means with unknown variance (standard deviation) but assumed equal
c. Two sample test of proportions
d. Single sample test of proportions
d. Single sample test of proportions
Consider the SAT question (problem 4) of the homework that is testing whether or not SAT
scores increased by at least 30 points after going through a program. The two errors that can be
made are to conclude that the program increases by at least 30 points even though they do not
and to conclude that the program fails to increase by at least 30 points even though it does. The
independent agency conducting the test has decided that the error of concluding the program
failed to hit its target when really the company can provide a 30 point increase is substantially
more important. This error would irreparably damage the company's reputation. They would
like to ensure that they do not make this error even if that means increasing the chance that
they falsely conclude the company provides its promised increase in score. When selecting their
alpha (choosing between 0.01, 0.05 and 0.10) which alpha level provides the highest -
answers✔✔a. Alpha = 0.01
b. Alpha = 0.05
c. Alpha = 0.10
, c. Alpha = 0.10
This is a Type II error; decreased as the significance level (alpha) is increased
I have two paired samples of means and should conduct a two sample hypothesis test of paired
means with unknown variance. If I instead conduct a two sample test of independent means
with unknown variance, I am more likely to reject the null hypothesis. - answers✔✔a. True
b. False
a. True
Higher variation and less power
A 20-minute consumer survey that included a $5 Starbucks gift card was emailed to 500 adults
aged 25-34. The survey resulted in 65 responses. The same 20-minute consumer survey was
emailed to 500 adults aged 25-34 without the Starbucks gift card. That survey resulted in 45
responses. We would like to know if the inclusion of a Starbucks gift card led to an increase in
survey response rate. Which of the following hypotheses should be used? (Assume that sample
1 is with the gift card and sample 2 is without the gift card). - answers✔✔a. H0: π1-π2=0; H1:
π1-π2≠0
b. H0: π1-π2≤0; H1: π1-π2>0
c. H0: μ1- μ2=0; H1: H0: μ1- μ2≠0
d. H0: μ1- μ2≥0; H1: H0: μ1- μ2<0
b. H0: π1-π2≤0; H1: π1-π2>0
A company has conducted a statistical two sample hypothesis test of means with known
variances with one tail. The critical value they used was +2.326 (alpha of 0.01). The test statistic
they calculated was 1.655 (pvalue of 0.049). Based on this, they decided to fail to reject the null
hypothesis. What can you say about their sensitivity to their choice of alpha? - answers✔✔a. If
they had selected a larger alpha (0.05 or 0.10), they would have rejected
b. If they had selected a larger alpha (0.05 or 0.10), they would have failed to reject
