Question 1

Suppose the population mean for a statistics test is 10 and the population standard deviation is 2. If you take a random sample of 50 students, what is the standard error of the mean ($$se$$)?

Accepted Answer

$$se = \frac{2}{\sqrt{50}} = 0.28284$$

Question 2

A researcher claims that Quebec residents have higher life satisfaction than the Canadian average of 42%. In a sample of 100 Quebec residents, 57% report high life satisfaction. What is the null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: p = 0.42$$

Question 3

Which of the following best describes the sampling distribution of the sample mean as the number of samples increases?

Accepted Answer

It becomes more normal and smooth, with skewness and kurtosis approaching zero.

Question 4

You sample 50 people at a conference and find their mean score on a statistics test is 11.9. The population mean is 10 and the population standard deviation is 2. What is the $$z-$$score for this sample mean?

Accepted Answer

$$z = \frac{11.9 - 10}{0.28284} = 6.72$$

Question 5

If you do not know the population standard deviation ($$\sigma$$), which test should you use to compare a sample mean to a population mean?

Accepted Answer

Single-sample $$t-$$test

Question 6

What is the formula for the degrees of freedom ($$df) in a $$single-sample $$t-$$test?

Accepted Answer

$$df = n - 1$$

Question 7

A poll finds that 37% of 1,507 registered voters approve of the president. In a sample of 20 friends, 30% approve. Which test should you use to compare these proportions?

Accepted Answer

Two-proportion $$z-$$test

Question 8

Which of the following is true about the $$\$$chi^2$$ (chi-square) distribution?

Accepted Answer

It is a family of distributions, typically used for right-tailed tests.

Question 9

If the standard deviation of midterm 1 is 20.277 and the standard deviation of the final is 15.041, which test would you use to determine if the variance significantly decreased?

Accepted Answer

Chi-square test for variance

Question 10

Which of the following statements about the standard error of the mean is correct?

Accepted Answer

It decreases as the sample size increases.

Question 11

Given a sample mean of 12, population mean of 10, sample standard deviation of 3, and sample size of 16, what is the $$t-$$statistic?

Accepted Answer

$$t = \frac{12 - 10}{3/\sqrt{16}} = \frac{2}{0.75} = 2.67$$

Question 12

Which of the following best describes the effect of increasing the number of replications in a sampling distribution?

Accepted Answer

The distribution becomes smoother and more closely approximates normality.

Question 13

If you want to construct a 95% confidence interval for a population mean with known $$\sigma$$, which critical value do you use?

Accepted Answer

$$z = 1.96$$

Question 14

Which of the following is NOT an assumption of the single-sample $$z-$$test?

Accepted Answer

The population standard deviation is unknown.

Question 15

A sample of 10 students has a mean score of 13, population mean is 10, and sample standard deviation is 4. What are the degrees of freedom for the $$t-$$test?

Accepted Answer

$$df = 9$$

Question 16

Which Excel function would you use to find the area to the right of a $$z-$$score of 2.5?

Accepted Answer

=NORM.S.DIST(2.5,FALSE)

Question 17

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we sampled repeatedly, 95% of the intervals would contain the true population mean.

Mini-Textbook Study Notes: Hypothesis Testing with One Sample and Related Distributions

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