Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

A claim made about a population parameter, representing the default assumption or status quo.

Question 2

A university claims the average SAT math score of incoming freshmen is 600. A researcher collects a random sample of 40 students and finds a sample mean of 622. The population standard deviation is 70. Using $$\alpha = 0.05$$, which test statistic should be used?

Accepted Answer

Use the $$z$$ statistic: $$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$$

Question 3

A tech company claims 90% of its devices pass inspection. A quality inspector tests 200 devices, 172 of which pass. At the $$\alpha = 0.01$$ significance level, what is the correct formula for the test statistic?

Accepted Answer

$$z = \frac{p̂ - p}{\sqrt{p(1-p)/n}}$$

Question 4

Which scenario describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$true.

Question 5

A cereal packaging line requires the fill-weight variance to be no greater than $$0.25 g$^2. A $$sample of 30 boxes yields a sample variance of $$0.31 g$^2. $$Which test statistic should be used to test if the population variance is greater than $$0.25 g$^2$$?

Accepted Answer

$$\$$chi^2$$ = \frac{(n-1)s^2$}{\$$sigma^2$$}$$

Question 6

A nutritionist believes the average daily protein intake for adults is 50g. A random sample of 37 adults has a sample mean of 51g and sample standard deviation of 6g. What is the correct formula for the test statistic if $$\sigma is $$unknown?

Accepted Answer

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

Question 7

Which of the following best describes the P-value in hypothesis testing?

Accepted Answer

The probability of obtaining a sample statistic as extreme as the observed one, assuming $$H_0 is $$true.

Question 8

A school claims that 30% of its students participate in after-school sports. A survey of 200 students finds that 72 participate. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{72}{200}$$

Question 9

A city government claims that no more than 25% of households have solar panels. A researcher surveys 200 households and finds that 62 have solar panels. What are the null and alternative hypotheses?

Accepted Answer

$$H_0$$: p = 0.25$$, H_a$$: p \u003e 0.25$$

Question 10

Which of the following statements about critical values is TRUE?

Accepted Answer

The critical value is the boundary of the rejection region.

Question 11

A soda company claims its cans contain 355 mL on average, but a sample of 50 cans has a mean of 352 mL. The population standard deviation is 5 mL. Using $$\alpha = 0.01$$, what is the correct formula for the test statistic?

Accepted Answer

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

Question 12

Which of the following would minimize the probability of a Type I error?

Accepted Answer

Decreasing $$\alpha$$

Question 13

A machine produces ball bearings designed to have a diameter standard deviation of 0.04 mm. An engineer suspects the variability has increased. A sample of 60 bearings shows a standard deviation of 0.052 mm. What is the null hypothesis?

Accepted Answer

$$H_0$$: \$$sigma^2$$ = $$0.04^2$$

Question 14

A fitness researcher claims that the average resting heart rate of yoga instructors is lower than the general adult population average of 72 bpm. Which alternative hypothesis is correct?

Accepted Answer

$$H_a: \mu \u003c 72$$

Question 15

A popular theme park claims weekly attendance is 100,000. You believe attendance is different. What is the correct form of the alternative hypothesis?

Accepted Answer

$$H_a: \mu 
eq 100,000$$

Question 16

Which of the following is NOT a step in the hypothesis testing process?

Accepted Answer

Calculate the population mean

Question 17

A business journal wants to prove that greater than 20% of companies have a female CEO. What is the correct null hypothesis?

Accepted Answer

$$H_0$$: p = 0.20$$

Question 18

If the claimed value is OUTSIDE the confidence interval, what is the correct conclusion for a two-tailed hypothesis test?

Accepted Answer

Reject the null hypothesis

Hypothesis Testing: Steps, Methods, and Applications

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