Question 1

A university claims that 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 null and alternative hypothesis for this test?

Accepted Answer

$$H_0$$: \mu = 600$$, H_a$$: \mu \u003e 600$$

Question 2

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

Accepted Answer

$$\hat{p} = \frac{172}{200} = 0.86$$

Question 3

Which test statistic should be used to test a claim about a population mean when the population standard deviation $$\sigma is $$unknown and the sample size is 20?

Accepted Answer

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

Question 4

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 hypothesis test should be performed?

Accepted Answer

$$H_0$$: \$$sigma^2 = 0.25$, H_a$$: \$$sigma^2$$ \u003e 0.25$$

Question 5

A local park claims that less than 15% of visitors litter. A random sample of 120 visitors finds that 25 litter. What is the correct test statistic for this hypothesis test?

Accepted Answer

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

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 alternative hypothesis if the nutritionist wants to test if the true mean differs from 50g?

Accepted Answer

$$H_a: \mu 
eq 50$$

Question 7

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 8

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

Accepted Answer

$$H_0$$: p = 0.20$$, H_a$$: p \u003e 0.20$$

Question 9

A sample of 50 cans of soda has a mean volume of 352 mL. The company claims the mean is 355 mL, with a known standard deviation of 5 mL. What is the $$z-$$test statistic for this sample?

Accepted Answer

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

Question 10

If the $$P-$$value for a hypothesis test is 0.03 and the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is enough evidence to support $$H_a$$

Question 11

A machine produces ball bearings with a designed standard deviation of 0.04 mm. A sample of 60 bearings shows a standard deviation of 0.052 mm. What is the correct test statistic for testing if the variability has increased?

Accepted Answer

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

Question 12

Which of the following statements about the critical value in hypothesis testing is TRUE?

Accepted Answer

The critical value is the boundary of the rejection region.

Question 13

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 14

Which of the following would decrease the probability of a Type I error in a hypothesis test?

Accepted Answer

Decreasing $$\alpha$$

Question 15

A hypothesis test for a population mean is performed at the 0.01 significance level. The 99% confidence interval for the mean does NOT contain the claimed value. What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is enough evidence to support $$H_a$$

Question 16

A fast-food chain wonders if the proportion of orders with drinks is less than 0.87. They collect a random sample of 80 orders and find 68 include drinks. What is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: p = 0.87$$, H_a$$: p \u003c 0.87$$

Question 17

A researcher claims that the average height of adult males in a city is 70 inches. She samples 12 adult males and finds a sample mean of 67.8 inches with a sample standard deviation of 2.1 inches. What is the degrees of freedom for the $$t-$$test?

Accepted Answer

$$df = 11$$

Hypothesis Testing for Population Proportions and Means: Structured Study Notes

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