Q: 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 correct null and alternative hypothesis for this test?

$$H_0$$: p = 0.3$$, H_a$$: p \neq 0.3$$

Question 1

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

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 its incoming freshmen is 600. A researcher collects a random sample of 40 students and finds a sample mean SAT math score of 622. The population standard deviation is known to be 70. Using a significance level of $$\alpha = 0.05$$, what is the correct test statistic to use?

Accepted Answer

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

Question 3

A tech company claims that 90% of its devices pass inspection. A quality inspector tests 200 devices, 172 of which passed. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{172}{200}$$

Question 4

Which formula is used to calculate the test statistic for a hypothesis test regarding a population proportion?

Accepted Answer

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

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

In hypothesis testing, what does the P-value represent?

Accepted Answer

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

Question 7

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. Which test statistic should be used?

Accepted Answer

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

Question 8

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

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 9

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 correct null and alternative hypothesis for this test?

Accepted Answer

$$H_0$$: p = 0.3$$, H_a$$: p 
eq 0.3$$

Question 10

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. What is the correct formula for the test statistic?

Accepted Answer

$$z = \frac{352 - 355}{5/\sqrt{50}}$$

Question 11

Which of the following is NOT a step in the four-step hypothesis testing procedure?

Accepted Answer

Calculate confidence interval

Question 12

A machine produces ball bearings with a designed 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 correct null hypothesis?

Accepted Answer

$$H_0$$: \$$sigma^2 = 0.0016$

Question 13

If the significance level $$\alpha is $$decreased, what happens to the probability of a Type I error?

Accepted Answer

It decreases.

Question 14

A city claims that 40% of households have backyard gardens. A researcher surveys 150 households and finds 72 with gardens. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{72}{150}$$

Question 15

Which of the following statements about critical values is TRUE?

Accepted Answer

The critical value is the boundary of the rejection region.

Question 16

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

Accepted Answer

$$H_a: \mu \u003c 72$$

Question 17

Which formula is used to calculate the test statistic for a hypothesis test regarding a population mean when the population standard deviation is unknown?

Accepted Answer

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

Question 18

A public health agency claimed last year that the proportion of children vaccinated for measles met their goal of 85%. They want to test if the current proportion falls shy of that goal. Which is the more serious error in this context?

Accepted Answer

Type II error: Failing to detect that the proportion is less than 85% when it actually is.

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