Question 1

A snack food company claims that their new packaging machine fills bags with an average of 454 grams of pretzels. A quality control analyst collects a random sample of 16 bags and finds a sample mean of 453 grams with a sample standard deviation of 2 grams. Which of the following is the correct null hypothesis ($$H_0) $$for testing if the machine is accurate?

Accepted Answer

$$H_0$$: \mu = 454$$

Question 2

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

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$actually true

Question 3

A medical researcher is testing whether a new drug lowers blood pressure more than the current standard. The null hypothesis is $$H_0$$: \mu = 120$$ mmHg. The alternative hypothesis is H_a$$: \mu \u003c 120$$ mmHg. What type of test is this?

Accepted Answer

Left-tailed test

Question 4

Suppose you conduct a hypothesis test at $$\alpha = 0.05$$ and obtain a $$P-$$value of $$0.03. $$What is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 5

Which of the following statements about the $$P-$$value is correct?

Accepted Answer

The $$P-$$value is the probability of obtaining a test statistic as extreme as the observed one, assuming $$H_0 is $$true.

Question 6

A car manufacturer claims their new engine has improved fuel efficiency. The previous mean was 26 mpg. A sample of 12 cars with the new engine has a mean of 27.5 mpg and a standard deviation of 3.5 mpg. What is the correct test statistic for testing $$H_0$$: \mu = 26$$?

Accepted Answer

$$t = \frac{27.5 - 26}{3.5/\sqrt{12}}$$

Question 7

If the power of a test is $$0.90$$, what does this mean?

Accepted Answer

There is a 90% probability of correctly rejecting $$H_0$$ when $$H_0 is $$false.

Question 8

A researcher is testing $$H_0$$: \mu = 50$$ vs H_a$$: \mu 
eq 50$$ using a sample of n=25$, sample mean $$\bar{x}=52$$, and sample standard deviation s=4$. What is the value of the t$-statistic?

Accepted Answer

$$t = \frac{52 - 50}{4/\sqrt{25}} = 2.5$$

Question 9

Which of the following best describes the relationship between confidence intervals and hypothesis tests for a population mean?

Accepted Answer

If the confidence interval does not contain the hypothesized mean, we reject $$H_0.$$

Question 10

A researcher runs 1,000 hypothesis tests at $$\alpha = 0.05. If $$all null hypotheses are true, about how many Type I errors are expected?

Accepted Answer

50

Question 11

Which of the following is an example of a two-tailed alternative hypothesis?

Accepted Answer

$$H_a: \mu 
eq 100$$

Question 12

Suppose you are testing $$H_0$$: \mu = 200$$ vs H_a$$: \mu \u003e 200$$ at $$\alpha = 0.01$$. You obtain a P$-value of 0.015$. What is the correct conclusion?

Accepted Answer

Fail to reject $$H_0$$

Question 13

Which of the following statements about statistical significance and practical significance is true?

Accepted Answer

A result can be statistically significant but not practically significant if the sample size is large.

Question 14

In the $$t-$$test for a population mean when $$\sigma is $$unknown, which formula is used for the test statistic?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{s/\sqrt{n}}$$

Question 15

A sample of 24 consumers in the Northeast has a mean annual spending of $$1,923$$ with a sample standard deviation of $$351. $$The national average is $$1,736. $$What is the $$t-$$statistic for testing if the Northeast is different from the national average?

Accepted Answer

$$t = \frac{1923 - 1736}{351/\sqrt{24}}$$

Question 16

Which of the following best describes the rejection region in hypothesis testing?

Accepted Answer

The set of values for the test statistic that leads to rejection of the null hypothesis

Question 17

If a test statistic falls exactly on the critical value in a two-tailed test, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 18

A researcher is testing $$H_0$$: \mu = 100$$ vs H_a$$: \mu \u003e 100$$ using a sample of n=10$, sample mean $$\bar{x}=105$$, and sample standard deviation s=5$. What is the t$-statistic?

Accepted Answer

$$t = \frac{105 - 100}{5/\sqrt{10}} = 3.16$$

Question 19

Which of the following is the correct interpretation of $$\alpha in $$hypothesis testing?

Accepted Answer

$$\alpha is $$the probability of making a Type I error

Hypothesis Tests Regarding a Parameter: Structured Study Notes

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