Some multiple choice questions in Statistics

A researcher claims that 82% of voters favor gun control. Identify the alternative hypothesis.

H0: p not equal to 0.82

H1: p < 0.82

H1: p not equal to 0.82

H0: p = 0.82

Question 2 5 pts

A psychologist claims that more than 52 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, which of the following sentences most correctly states the conclusion?

There is sufficient evidence to support the claim that the true proportion is less than 52%

There is not sufficient evidence to support the claim that the true proportion is less than 52%

There is sufficient evidence to support the claim that the true proportion is greater than 52%

There is not sufficient evidence to support the claim that the true proportion is greater than 52%

Question 3 5 pts Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 for a right-tailed test.

Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 for a right-tailed test.

+1.96

+/- 1.96

		+/- 1.645
+1.645

Question 4 5 pts

Find the value of the test statistic given the following information. A researcher claims that the proportion of drowning deaths attributable to beaches is more than 0.25. The sample statistics include n=552 drowning deaths with 30% of them attributable to beaches.

–	2.71
2.56

2.71

-2.56

Question 5 5 pts

Identify the null and alternative hypotheses given the following information. The owner of a baseball team claims that the average attendance at games is at least 30,000.

[removed]

H0: µ, the average attendance at games, is equal to 30,000 H1: µ, the average attendance at games, is less than 30,000

H0: µ, the average attendance at games, is greater than 30,000 H1: µ, the average attendance at games, is less than or equal to 30,000

H0: µ, the average attendance at games, is greater than or equal to 30,000 H1: µ, the average attendance at games, is less than 30,000

H0: µ, the average attendance at games, is less than 30,000 H1: µ, the average attendance at games, is greater than or equal to 30,000

Question 6 5 pts

A claim is made that the proportion of kids who play sports is less than 0.48, and the sample statistics include n=120 subjects with 36% saying that they play a sport. Find the value of the test statistic.

-2.63

57.69

-7.60

-8.32

Question 7 5 pts Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 for a two-tailed test.

Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 for a two-tailed test.

+/- 2.575

+/- 1.764

+/- 1.645 +/- 1.96

Question 8 5 pts

A manufacturer makes refrigerators that are supposed to maintain a true mean temperature of 41 degrees F. A consumer group claims they can prove that the true mean temperature does not equal 41 degrees. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, which of the following sentences most correctly states the conclusion?

There is not sufficient evidence to support the claim that µ equals 41 deg.F

There is not sufficient evidence to support the claim that µ does not equal 41 deg.F

There is sufficient evidence to support the claim that µ equals 41 deg.F

There is sufficient evidence to support the claim that µ does not equal 41 deg.F

Question 9 5 pts Identify the null and alternative hypotheses given the following information. The principal of a middle school claims that test scores of 7^th graders at her school have a standard deviation less than 12.

Identify the null and alternative hypotheses given the following information. The principal of a middle school claims that test scores of 7th graders at her school have a standard deviation less than 12.

H0: sigma >= 12 ; H1: sigma <12

H0: sigma < 12 H1: sigma > 12

H0: sigma < 12: sigma >= 12

H0: sigma = 12 ; H1: sigma not equal to 12

Question 10 5 pts Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 for a left-tailed test

Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 for a left-tailed test

+/- 1.645

-1.645

		+/- 1.96
	-1.96

Question 11 5 pts

Identify the null and alternative hypotheses given the following information. A cereal company claims that the weight of the cereal in its boxes is at least 16 ounces.

H0: µ = 16 oz. ; H1: µ not equal to 16 oz.

H0: µ >= 16 oz. ; H1: µ < 16 oz.

H0: µ < 16 oz. : H1 µ >= 16 oz.

H0: µ > 16 oz.; H1: µ <= 16 oz.

Question 12 5 pts

A researcher claims that men, on average, can’t even wait 5.5 seconds without pressing a button on the tv remote control (i.e., time between remote control use). Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion is nontechnical terms.

Fail to reject H0. There is not sufficient evidence to support the claim that the average time between pressing remote control buttons is less than 5.5 seconds for men.

Reject H0. There is not sufficient evidence to warrant rejection of the claim that the average time between pressing remote control buttons is greater than or equal to 5.5 seconds for men.

Reject H0. There is sufficient evidence to support the claim that the average time between pressing remote control buttons is less than 5.5 seconds for men.

Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the average time between pressing remote control buttons is less than 5.5 seconds for men.

Question 13 5 pts

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is no more than (i.e. less than or equal to) 4 in every one thousand (0.4% or 0.004). Identify the null and alternative hypotheses.

[removed]

H0: p >= 0.004 ; H1: p < 0.004

H0: p < 0.004 H1: p >= 0.004

[removed]

H0: p = 0.004 ; H1: p not equal to 0.004

H0: p <= 0.004 1: p > 0.004

Question 14 5 pts

The principal of a middle school claims that test scores of 7th graders at his school vary no more than (i.e., less than or equal to) the test scores of 7th graders at a neighboring school, which have a standard deviation of 12. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, which of the following sentences most correctly states the conclusion?

There is sufficient evidence to support the claim that sigma > 12

There is sufficient evidence to warrant rejection of the claim that sigma <= 12

There is sufficient evidence to support the claim that sigma <= 12

There is not sufficient evidence to support the claim that sigma > 12

Question 15 5 pts

An entomologist (i.e., scientist who studies insects) writes an article which claims that fewer than 15 in ten thousand black widow spiders are unable to produce venom due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, which of the following sentences most correctly states the conclusion?

There is sufficient evidence to support the claim that p < 15/10000

There is sufficient evidence to support the claim that p > 15/10000

There is not sufficient evidence to support the claim that p < 15/10000

There is not sufficient evidence to support the claim that p > 15/10000

Question 16 5 pts

Megan Motor Company claims that its new car, the Mumps, will average more than 35 miles per gallon. Identify the null and alternative hypotheses.

H0: µ > 35 ; H1: µ <= 35

H0: µ <= 35 H1: µ > 35

H0: µ = 35 ; H1: µ not equal to 35

H0: µ< 35 H1: µ >= 35

Question 17 5 pts Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 and H1 is mu not equal to 5.55.

Assume the data are normally distributed and n > 50. Find the critical z value(s) used to test a null hypothesis where alpha = 0.05 and H1 is mu not equal to 5.55.

+/- 1.96

+/- 1.75

-1.96

+/-1.64

Question 18 5 pts Find the critical value(s) of chi-squared based on H1: sigma > 3.5, n=14, alpha = 0.05

Find the critical value(s) of chi-squared based on H1: sigma > 3.5, n=14, alpha = 0.05

23.685

22.362

5.892

24.736

Question 19 5 pts

A cereal company claims that the mean weight of the cereal in their boxes is at least 16 ounces. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, which of the following sentences most correctly states the conclusion?

There is sufficient evidence to warrant rejection of the claim that mu < 16 oz.

There is not sufficient evidence to warrant rejection of the claim that mu >= 16 oz.

There is not sufficient evidence to warrant rejection of the claim that mu < 16 oz.

There is sufficient evidence to warrant rejection of the claim that mu >= 16 oz.

Question 20 5 pts Find the critical value(s) of chi-squared based on H1: sigma < 0.777, n=19, alpha = 0.025.

Find the critical value(s) of chi-squared based on H1: sigma < 0.777, n=19, alpha = 0.025.

8.907

7.015

8.231

31.526

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