Q: Given the following hourly rates charged by mechanic shops: 55, 69, 65, 72, 49, 59, 65, 75, 89, 75, 79, 58, 77, 60, 52, 74, 64, 55, 59. Using the Sign Test, what is the alternative hypothesis to test if the median is greater than $$59/hr$$?

$$H_1$$: \text{median} \u003e 59$$

Question 1

Why are non-parametric tests used in statistics?

Accepted Answer

Because they do not assume a specific population distribution and are useful when data are ordinal or not normally distributed.

Question 2

What does ANOVA stand for, and what is its primary use?

Accepted Answer

Analysis of Variance; used to compare the means of three or more groups.

Question 3

A 'Goodness of Fit' test is used to:

Accepted Answer

Test whether observed frequencies match expected frequencies for a categorical variable.

Question 4

Suppose you want to test if the likelihood of earning an 'A' in a class is the same for all seating rows. Which statistical test is most appropriate?

Accepted Answer

Chi-square goodness of fit test

Question 5

Given the following contingency table for a drug effectiveness study:

Drug: Lower pressure = 155, No improvement = 45
Placebo: Lower pressure = 56, No improvement = 40

Which test should be used to determine if the reduction in blood pressure is dependent on taking the drug?

Accepted Answer

Chi-square test for independence

Question 6

You are given the number of traffic tickets issued on four streets over several days. To test if the mean number of tickets is the same for all streets at a 0.10 significance level, which test should you use?

Accepted Answer

One-way ANOVA

Question 7

A random sample of 24 college graduates found that 8 work in a field related to their major. Using a sign test at the 0.10 significance level, what is the null hypothesis?

Accepted Answer

$$H_0$$: p = 0.5$$

Question 8

A company implements a training program to reduce sexual harassment claims. The number of claims before and after training in 10 countries is recorded. Which non-parametric test is most appropriate to analyze if the training was effective?

Accepted Answer

Sign Test

Question 9

Given the following hourly rates charged by mechanic shops: 55, 69, 65, 72, 49, 59, 65, 75, 89, 75, 79, 58, 77, 60, 52, 74, 64, 55, 59. Using the Sign Test, what is the alternative hypothesis to test if the median is greater than $$59/hr$$?

Accepted Answer

$$H_1$$: 	ext{median} \u003e 59$$

Question 10

Which of the following is a key assumption of the Wilcoxon Signed-Ranks Test?

Accepted Answer

The data are paired and come from a symmetric distribution.

Question 11

A study collects GPA and ACT scores for 7 students. Which statistical method is most appropriate to test for a linear relationship between GPA and ACT?

Accepted Answer

Pearson correlation coefficient hypothesis test

Question 12

If the correlation coefficient $$r$$ between GPA and ACT scores is $$0.85$$, what does this indicate?

Accepted Answer

There is a strong positive linear relationship between GPA and ACT scores.

Question 13

What does the coefficient of determination $$r^2$$ represent in the context of a regression analysis between GPA and ACT scores?

Accepted Answer

The proportion of variance in ACT scores explained by GPA.

Question 14

Given a regression equation $$y = 5x + 10$$, where $$x is $$GPA and $$y is $$ACT score, what does the slope of 5 mean?

Accepted Answer

For each one-point increase in GPA, the ACT score is predicted to increase by 5 points.

Question 15

Using the regression equation $$y = 4x + 12$$, predict the ACT score for a student with a GPA of 3.5.

Accepted Answer

$$y = 4 	imes 3.5 + 12 = 26$$

Question 16

A 95% confidence interval for a predicted ACT score is (24, 28). What does this mean?

Accepted Answer

We are 95% confident that the true ACT score for a student with the given GPA falls between 24 and 28.

Question 17

If you use a regression equation derived from data with GPA values between 2.0 and 4.0 to predict the GPA for a student with an ACT score of 8, what is the main concern?

Accepted Answer

The prediction is unreliable because it is an extrapolation outside the range of the data.

Question 18

Which of the following is NOT an assumption of ANOVA?

Accepted Answer

The samples are paired.

Question 19

In a chi-square goodness of fit test, how are the expected frequencies calculated?

Accepted Answer

By multiplying the total sample size by the hypothesized proportion for each category.

Statistics Exam Study Guidance: Hypothesis Testing, ANOVA, Nonparametric Tests, Correlation, and Regression

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