Question 1

An economist wishes to compare retirement savings of public sector workers to private sector workers. What type of hypothesis test should she employ?
A) a one-sample, one-tailed hypothesis test
B) a one-sample, two-tailed hypothesis test
C) a contingency table analysis
D) a two-sample hypothesis test

Accepted Answer

The economist is comparing two independent groups (public sector workers and private sector workers), so a two-sample hypothesis test is appropriate to determine if there is a significant difference in retirement savings between the two groups.

Question 2

When testing for the significance of the difference between two samples, what is the proper assumption for step 1?
A) The samples are random only.
B) The samples are dependent and random.
C) The samples are independent only.
D) The samples are independent and random.

Accepted Answer

The proper assumption for testing the significance of the difference between two samples is that the samples are independent and random. This ensures that the results are not biased and that the samples are representative of the populations being compared.

Question 3

A sample is gathered from one country, and a second sample is gathered from another country. If the sampling conducted from country 1 had no bearing on the sampling conducted in country 2, what would we call this?
A) independent random sampling
B) dependent random sampling
C) pooled hypothesis sampling
D) alpha random sampling

Accepted Answer

The samples are considered independent because the selection of one sample does not affect the selection of the other.

Question 4

Educational researchers wish to compare students from two school districts (Brownsville School District and Midlands School District) on their levels of scientific literacy. They provide all students with the same test and calculate average scores for each sample. What would be an appropriate null hypothesis?
A) The sample of Midlands students are no different from the sample of Brownsville students.
B) Mean levels of scientific literacy are equal across both school districts.
C) Mean levels of scientific literacy are equal across both samples.
D) The population variance for scientific literacy is equal across both school districts.

Accepted Answer

The null hypothesis in this context would state that there is no difference in the mean levels of scientific literacy between the two school districts.

Question 5

What pieces of information from two samples does the "pooled estimate" combine?
A) Z (obtained) scores for each sample
B) means of both sampling distributions
C) the difference in means between the two samples
D) sample standard deviations, divided by the size of each sample (n)

Accepted Answer

The "pooled estimate" combines the sample standard deviations, divided by the size of each sample (n), to estimate a common standard deviation when assuming equal variances in two samples.

Question 6

Why must we typically use the formula instead of using ó₁ and ó₂ when conducting a two-sample hypothesis test? A) because the standard deviations from the relevant populations (ó₁ and ó₂) are seldom known B) because ó₁ and ó₂ are based on the sampling distribution, which is biased C) because ó₁ and ó₂ can be used only for nominal level variables D) because ó₁ and ó₂ increase the risk of Type I error

Accepted Answer

The answer of Why must we typically use the formula...

Question 7

When testing for the significance of the difference between two sample means, which of the following must be estimated before computing the test statistic?
A) the critical region
B) the standard deviation of the sampling distribution
C) the standard deviations of the samples
D) the population means

Accepted Answer

The standard deviation of the sampling distribution, also known as the standard error, must be estimated to compute the test statistic for the difference between two sample means.

Question 8

When testing for the significance of the difference between two sample means, which of the following is used to estimate the standard deviation of the sampling distribution?
A) sample standard deviations corrected for bias
B) the standard error of the means
C) population standard deviations
D) degrees of freedom

Accepted Answer

The sample standard deviations corrected for bias are used to estimate the standard deviation of the sampling distribution.

Question 9

Random samples of persons living in urban and suburban areas have been given a scale that measures their support for gun control. Persons residing in urban areas average 10.2 with a standard deviation of 5.3. Persons residing in suburban areas also average 10.2, but the standard deviation is 1.8. What is the appropriate way to deal with these results?
A) Do not conduct any tests: because the sample means are the same value, these results cannot be significant.
B) Test the difference in the sample means for statistical significance.
C) Use a test of significance with a very high alpha level (á > 0.10).
D) Use a one-tailed test of significance.

Accepted Answer

The answer of Random samples of persons living in urban...

Question 10

The mean of group 1 (n = 50) is 100, and the mean of group 2 (n = 60) is 90. Both samples have a standard deviation of 20. What is the appropriate value for the test statistic?
A) alpha
B) 50 + 60 = 110
C) 100 - 90 = 10
D) 20 - 20 = 0

Accepted Answer

The test statistic for comparing two means is based on the difference between the means, which is 100 - 90 = 10.

Question 11

Which of these variables would be appropriate for testing the difference between two sample means?
A) gender
B) height, in inches
C) social class (lower, middle, upper)
D) make and model of car

Accepted Answer

Height, in inches, is a continuous variable that can be used to test the difference between two sample means.

Question 12

A random sample of Toronto car commuters is compared to a random sample of Toronto bike commuters. After analyzing post-commute stress levels, researchers fail to reject the null hypothesis. Which of the following could they conclude?
A) Car commuters and bike commuters differ significantly in their levels of post-commute stress.
B) Car commuters are more stressed after their commutes than are bike commuters.
C) The difference between the groups is significant, but it is impossible to determine which group is more stressed.
D) Any difference in stress between car commuters and bike commuters is no greater than could have occurred by chance alone.

Accepted Answer

Failing to reject the null hypothesis suggests that any observed difference in stress levels between the two groups is not statistically significant and could be due to random chance.

Question 13

Demographers test whether immigrants or native-born Canadians have higher fertility rates. They obtain sample statistics from both populations and obtain a Z (obtained) score of 2.02 in the comparison of means. Under what conditions could they reject the null hypothesis, assuming a two-tailed test?
A) only if alpha was set at 0.05: Z (critical) = ±1.96
B) only if alpha was set at 0.01: Z (critical) = ±2.33
C) only if alpha was set at 0.001: Z (critical) = ±2.58
D) The null hypothesis would be rejected at any alpha value.

Accepted Answer

The obtained Z score of 2.02 is greater than the critical value of ±1.96 for a two-tailed test with alpha set at 0.05, allowing the null hypothesis to be rejected.

Question 14

When testing for the significance of the difference between sample means when  (sigma) is unknown, which of the following is the proper sampling distribution?
A) the Z distribution
B) the beta distribution
C) the t distribution
D) the alpha distribution

Accepted Answer

The answer of When testing for the significance of the...

Question 15

Which population parameter is assumed to be approximately equal for a two-sample hypothesis test using the t distribution?
A) population means
B) population variances
C) sampling distributions
D) population sizes

Accepted Answer

In a two-sample t-test, it is assumed that the population variances are approximately equal, which is known as the assumption of homogeneity of variance.

Question 16

Researchers conduct a test of mean differences using the t distribution with sample sizes of 30 and 35. The researchers specify a two-tailed test and set alpha at 0.05. What is the degrees of freedom they need to obtain the critical value for their test?
A) 29
B) 34
C) 63
D) 65

Accepted Answer

The degrees of freedom for a two-sample t-test is calculated as the sum of the sample sizes minus 2, which is (30 + 35 - 2) = 63.

Question 17

Which of these sets of samples would qualify as meeting the assumption of sample size equality for calculating a "pooled estimate" in a two-sample hypothesis test?
A) sample 1: n = 200; sample 2: n = 45
B) sample 1: n = 500; sample 2: n = 300
C) sample 1: n = 800; sample 2: n = 350
D) sample 1: n = 1500; sample 2: n = 650

Accepted Answer

For a pooled estimate, the sample sizes should be relatively similar. Option B has the closest sample sizes, making it the most suitable for a pooled estimate.

Question 18

Under which of these circumstances is the assumption of equal population variance safe to assume in a two-sample hypothesis test?
A) when both samples are greater than n = 100
B) when both samples are approximately equal in size
C) when the difference in means between the two samples is statistically significant
D) when the ratio of the sample standard deviation is smaller than 2

Accepted Answer

When both samples are approximately equal in size, the assumption of equal population variance is safe to assume in a two-sample hypothesis test.

Question 19

Which of these examples of the two-sample hypothesis test will have the greatest degrees of freedom?
A) sample 1: mean = 1600, standard deviation = 500, n = 45; sample 2: mean = 1200, standard deviation = 200, n = 85
B) sample 1: mean = 3.2, standard deviation = 0.7, n = 155; sample 2: mean = 4.6, standard deviation = 0.9, n = 25
C) sample 1: mean = 44, standard deviation = 8, n = 1400; sample 2: mean = 42, standard deviation = 10, n = 500
D) sample 1: mean = 122, standard deviation = 46, n = 900; sample 2: mean = 153, standard deviation = 38, n = 1300

Accepted Answer

The degrees of freedom for a two-sample t-test is calculated as the sum of the sample sizes minus 2 (n1 + n2 - 2). Option D has the largest combined sample size (900 + 1300 = 2200), resulting in the greatest degrees of freedom.

Question 20

From the population of a university, random samples of 45 graduate students and 37 undergraduate students were given a scale that measures sexual experiences. The undergraduate students report an average of 1.6 sexual partners over their lifetimes, while the graduate students report an average of 2.5 partners. The t (obtained) for this difference was -3.56, and the t (critical) was ±2.34. Which of the following can be concluded from these observations?
A) that sexual mores are deteriorating
B) that undergraduate students are more sexually active
C) that graduate students and undergraduate students are significantly different in their sexual experiences
D) that no significant difference exists between graduate students and undergraduate students

Accepted Answer

The obtained t-value of -3.56 exceeds the critical t-value of ±2.34, indicating a statistically significant difference in sexual experiences between graduate and undergraduate students.

Quiz 11: Hypothesis Testing With Means and Proportions: The Two-Sample Case

An economist wishes to compare retirement savings of public sector workers to private sector workers. What type of hypothesis test should she employ?

When testing for the significance of the difference between two samples, what is the proper assumption for step 1?

A sample is gathered from one country, and a second sample is gathered from another country. If the sampling conducted from country 1 had no bearing on the sampling conducted in country 2, what would we call this?

What pieces of information from two samples does the "pooled estimate" combine?

Why must we typically use the formula instead of using ó1 and ó2 when conducting a two-sample hypothesis test?

When testing for the significance of the difference between two sample means, which of the following must be estimated before computing the test statistic?

When testing for the significance of the difference between two sample means, which of the following is used to estimate the standard deviation of the sampling distribution?

The mean of group 1 (n = 50) is 100, and the mean of group 2 (n = 60) is 90. Both samples have a standard deviation of 20. What is the appropriate value for the test statistic?

Which of these variables would be appropriate for testing the difference between two sample means?

A random sample of Toronto car commuters is compared to a random sample of Toronto bike commuters. After analyzing post-commute stress levels, researchers fail to reject the null hypothesis. Which of the following could they conclude?

Demographers test whether immigrants or native-born Canadians have higher fertility rates. They obtain sample statistics from both populations and obtain a Z (obtained) score of 2.02 in the comparison of means. Under what conditions could they reject the null hypothesis, assuming a two-tailed test?

When testing for the significance of the difference between sample means when (sigma) is unknown, which of the following is the proper sampling distribution?

Which population parameter is assumed to be approximately equal for a two-sample hypothesis test using the t distribution?

Researchers conduct a test of mean differences using the t distribution with sample sizes of 30 and 35. The researchers specify a two-tailed test and set alpha at 0.05. What is the degrees of freedom they need to obtain the critical value for their test?

Which of these sets of samples would qualify as meeting the assumption of sample size equality for calculating a "pooled estimate" in a two-sample hypothesis test?

Under which of these circumstances is the assumption of equal population variance safe to assume in a two-sample hypothesis test?

Which of these examples of the two-sample hypothesis test will have the greatest degrees of freedom?

Why must we typically use the formula instead of using ó₁ and ó₂ when conducting a two-sample hypothesis test?