EBook Problems Hypothesis Basics

EBook Problems Set - Fundamentals of Hypothesis Testing

Problem 1

Suppose you were hired to conduct a study to find out which of two brands of soda college students think taste better. In your study, students are given a blind taste test. They rate one brand and then rated the other, in random order. The ratings are given on a scale of 1 (awful) to 5 (delicious). Which type of test would be the best to compare these ratings?

• Choose one answer.

(a) One-Sample t

(b) Chi-Square

(c) Paired Difference t

(d) Two-Sample t

{{hidden|Answer|(c)}

Problem 2

USA Today's AD Track examined the effectiveness of the new ads involving the Pets.com Sock Puppet (which is now extinct). In particular, they conducted a nationwide poll of 428 adults who had seen the Pets.com ads and asked for their opinions. They found that 36% of the respondents said they liked the ads. Suppose you increased the sample size for this poll to 1000, but you had the same sample percentage who like the ads (36%). How would this change the p-value of the hypothesis test you want to conduct?

• Choose One Answer.

(a) No way to tell

(b) The new p-value would be the same as before

(c) The new p-value would be smaller than before

(d) The new p-value would be larger than before

Answer

 (c)

Problem 3

A marketing director for a radio station collects a random sample of three hundred 18 to 25 year-olds and two hundred and fifty 25 to 40 year-olds. She records the percent of each group that had purchased music online in the last 30 days. She performs a hypothesis test, and the p-value of her test turns out to be 0.15. From this she should conclude:

• Choose one answer.

(a) that about 15% more people purchased on-line music in the younger group than in the older group.

(b) there is insufficient evidence to conclude that there is a difference in the proportion of on-line music purchases in the younger and older group.

(c) the proportion of on-line music purchasers is the same in the under-25 year-old group as in the older group.

(d) the probability of getting the same results again is 0.15.

Answer

 (b)

Problem 4

If we want to estimate the mean difference in scores on a pre-test and post-test for a sample of students, how should we proceed?

• Choose one answer.

(a) We should construct a confidence interval or conduct a hypothesis test

(b) We should collect one sample, two samples, or conduct a paired data procedure

(c) We should calculate a z or a t statistic

Answer

 (a)

Problem 5

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let mu denote the true average reflectometer reading for a new type of paint under consideration. A test of the null hypothesis that mu = 20 versus the alternative hypothesis that mu > 20 will be based on a random sample of size n from a normal population distribution. In which of the following scenarios is there significant evidence that mu is larger than 20?

(i) n=15, t=3.2, alpha=0.05

(ii) n=9, t=1.8, alpha=0.01

(iii) n=24, t=-0.2, alpha=0.01

• Choose one answer.

(a) (ii) and (iii)

(b) (i)

(c) (iii)

(d) (ii)

Answer

 (b)

Problem 6

The average length of time required to complete a certain aptitude test is claimed to be 80 minutes. A random sample of 25 students yielded an average of 86.5 minutes and a standard deviation of 15.4 minutes. If we assume normality of the population distribution, is there evidence to reject the claim? (Select all that applies).

• Choose at least one answer.

(a) No, because the probability that the null is true is > 0.05

(b) Yes, because the observed 86.5 did not happen by chance

(c) Yes, because the t-test statistic is 2.11

(d) Yes, because the observed 86.5 happened by chance

Answer

 (b)

Problem 7

We observe the math self-esteem scores from a random sample of 25 female students. How should we determine the probable values of the population mean score for this group?

• Choose one answer.

(a) Test the difference in means between two paired or dependent samples.

(b) Test that a correlation coefficient is not equal to 0 (correlation analysis).

(c) Test the difference between two means (independent samples).

(d) Test for a difference in more than two means (one way ANOVA).

(e) Construct a confidence interval.

(f) Test one mean against a hypothesized constant.

(g) Use a chi-squared test of association.

Answer

 (e)

Problem 8

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test where H0: the food is safe, and H1: the food is not A. If you are a consumer, which type of error would be the worst one for the inspector to make, the type I or type II error?

• Choose one answer.

(a) Type I

(b) Type II

Answer

 (b)

Problem 9

A college admissions officer is concerned that their admission criteria might not treat men and women with equal weight. To test this, the college took a random sample of male and female high school seniors from a very large local school district and determined the percent of males and females who would be eligible for admission at the college. Which of the following is a suitable null hypothesis for this test?

• Choose one answer.

(a) p = 0.5

(b) The proportion of all eligible men in the district will not equal the proportion of all eligible women in the district.

(c) The proportion of all eligible men in the school district should be equal to the proportion of all eligible women in the school district.

(d) The proportion of eligible men sampled should equal the propotion of eligible women sampled.

Answer

 (b)

Problem 10

The average blood pressure for adults in the 30-40 year old age range is about 135. A researcher wonders whether the blood pressure of individuals with high stress positions differs from 135, keeping age range constant.

For a random sample of 120 people with high stress jobs, he found: X_bar = 137 p-value = 0.11 95% CI (139 to 141)

Based on these findings, he decided not to reject the null. Did he make the right decision?

• Choose one answer.

(a) He did not make the right decision because his confidence interval does not include the hypothesized value under the null.

(b) The results reported by this researcher are inconsistent and contradictory.

(c) Yes, he made the right decision because the probability of rejecting the true null is 11%, and it is higher than the 5%.

(d) This researcher needs to report the standard deviation for his data.

Answer

 (b)

Problem 11

We want to determine if college GPAs differ for male athletes in major sports (e.g., football), minor sports (e.g., swimming), and intramural sports. What statistical method is most likely to be used to answer this question? Assume that all neccessary assumptions have been met for using this procedure.

• Choose one answer.

(a) Test one mean against a hypothesized constant

(b) Test the difference in means between two paired or dependent samples

(c) test for a difference in more than two means (one way ANOVA)

(d) Test that a correlation coefficient is not equal to 0, correlation analysis

(e) Test the difference between two means(independent samples)

Answer

 (c)

Problem 12

In a one-way ANOVA with 3 groups, a rejection of the null hypothesis implies that:

• Choose one answer.

(a) The 3 population means are equal to each other

(b) Each sample mean differs significantly from all other sample means

(c) Some subset of population means differs from some other subset of population means

(d) Each population mean differs significantly from all other population means

(e) The 3 sample means are equal to each other

Answer

 (d)

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