Q: A researcher compares the mean ACT scores of juniors and seniors. The sample means are 21.8 (juniors) and 22.9 (seniors), with standard deviations of 1.7 and 1.9, respectively. What is the correct alternative hypothesis for testing if seniors score higher than juniors?

$$H_1$$: \mu_{\text{senior}} \u003e \mu_{\text{junior}}$$

Question 1

A researcher wants to test whether the mean calcium level of healthy pregnant women differs from 9.5 mg/dL. A sample of 151 women has a mean of 9.7 mg/dL and a standard deviation of 0.7 mg/dL. Which of the following is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: \mu = 9.5$$

Question 2

A school reports that the mean ACT score for its students is 21.2 with a standard deviation of 5.0. If the national mean is 20.8, which test statistic should be used to determine if the school's mean is significantly different from the national mean?

Accepted Answer

$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$

Question 3

A consumer agency tests the lifespans (in hours) of 3 brands of lightbulbs. Which statistical test is most appropriate to determine if there is a significant difference in mean lifespan among the brands?

Accepted Answer

One-way ANOVA

Question 4

A researcher wants to know if there is a positive correlation between the cholesterol levels of husbands and wives. Which formula should be used to calculate the Pearson correlation coefficient?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 5

The Mars candy company claims that 7% of its M&Ms are orange. You buy a bag of 300 M&Ms and find that 30 are orange. Which test would you use to determine if the proportion of orange M&Ms is significantly different from the claimed value?

Accepted Answer

One-sample z-test for proportions

Question 6

A survey is conducted to see if the majority of all living alumni support a new football coach. Out of 1,000 randomly selected alumni, 610 support the coach. What is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: p = 0.5$$

Question 7

Researchers want to determine if stress levels differ between minorities and non-minorities. Which test is most appropriate if the data are approximately normally distributed and the groups are independent?

Accepted Answer

Independent samples t-test

Question 8

If you had used four racial categories (Caucasian, African American, Hispanic, Asian) instead of two, which statistical test would be most appropriate to compare mean stress levels among the groups?

Accepted Answer

One-way ANOVA

Question 9

A study examines whether the proportion of boys and girls who say making good grades is their most important goal differs. The data are: 152 boys and 243 girls say 'make good grades.' Which test should be used?

Accepted Answer

Chi-square test for independence

Question 10

A researcher wants to test if crawling age differs by birth month (January, May, September). The means and standard deviations are given for each group. Which test should be used to determine if there is a significant difference in mean crawling age among the months?

Accepted Answer

One-way ANOVA

Question 11

Suppose a researcher finds a P-value of 0.03 when testing $$H_0$$: \mu = 9.5$$ against H_1$: \mu 
eq 9.5 at$$ $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is significant evidence that the mean is not 9.5.

Question 12

A researcher compares the mean ACT scores of juniors and seniors. The sample means are 21.8 (juniors) and 22.9 (seniors), with standard deviations of 1.7 and 1.9, respectively. What is the correct alternative hypothesis for testing if seniors score higher than juniors?

Accepted Answer

$$H_1$$: \mu_{	ext{senior}} \u003e \mu_{	ext{junior}}$$

Question 13

Which of the following best describes a Type I error in the context of hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis

Question 14

A P-value is best described as:

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 15

Which of the following is the correct formula for a one-sample z-test for a population mean when the population standard deviation is known?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\frac{\sigma}{\sqrt{n}}}$$

Question 16

In a hypothesis test, if the significance level $$\alpha is $$set to 0.01, what does this mean?

Accepted Answer

There is a 1% chance of making a Type I error.

Question 17

A chi-square test for independence is most appropriate when:

Accepted Answer

You want to test if two categorical variables are related.

Question 18

Which of the following is NOT an assumption of the independent samples t-test?

Accepted Answer

The two samples are paired.

Question 19

A researcher finds a significant difference in mean crawling age among three birth months. What is the next appropriate step?

Accepted Answer

Conduct post-hoc pairwise comparisons to determine which groups differ.

Study Notes: Tests of Inference in Statistics

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