# MATH 221 Statistics for Decision Making Week 6 Homework

## MATH 221 Statistics for Decision Making Week 6 Homework

**MATH 221 Statistics for Decision Making ****Week 6 Homework **

Question 1A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 36 months. Write the null and alternative hypotheses and note which is the claim.

Ho: μ ≤ 36, Ha: μ > 36 (claim)

Ho: μ > 36, Ha: μ ≤ 36 (claim)

Ho: μ ≤ 36 (claim), Ha: μ > 36

Ho: μ = 36 (claim), Ha: μ ≥ 36

Question 2A business claims that the mean time that customers wait for service is at most 9.2 minutes. Write the null and alternative hypotheses and note which is the claim.

Ho: μ ≥ 9.2, Ha: μ ≤ 9.2 (claim)

Ho: μ > 9.2, Ha: μ ≤ 9.2 (claim)

Ho: μ > 9.2 (claim), Ha: μ > 9.2

Ho: μ ≤ 9.2 (claim), Ha: μ > 9.2

Question 3An amusement park claims that the average daily attendance is at least 15,000. Write the null and alternative hypotheses and note which is the claim.

>Ho: μ ≥ 15000 (claim), Ha: μ < 15000

Ho: μ = 15000, Ha: μ ≤ 15000 (claim)

Ho: μ ≤ 15000, Ha: μ > 15000 (claim)

Ho: μ > 15000 (claim), Ha: μ = 15000

Question 4A transportation organization claims that the mean travel time between two destinations is about 12 minutes. Write the null and alternative hypotheses and note which is the claim.

Ho: μ = 12 (claim), Ha: μ ≤ 12

Ho: μ = 12 (claim), Ha: μ ≠ 12

Ho: μ > 12, Ha: μ ≤ 12 (claim)

Ho: μ ≠ 12, Ha: μ = 12 (claim)

Question 5 Type I and type II errors occur because of what issue within the hypothesis testing process?

The population is not a representative subset of the sample

The sample mean is different than the population mean

The sample taken is not representative of the population

The math calculations were done incorrectly

Question 6A scientist claims that the mean gestation period for a fox is 51.5 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?

There is not enough evidence to support the scientist’s claim that the gestation period is more than 51.5 weeks

There is not enough evidence to support the scientist’s claim that the gestation period is 51.5 weeks

There is enough evidence to support the scientist’s claim that the gestation period is 51.5 weeks

The evidence indicates that the gestation period is less than 51.5 weeks

Question 7A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?

There is sufficient evidence to support the claim that less than 10% of the employees are paid minimum wage

There is sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage

There is not sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage

There is not sufficient evidence to support the claim that 10% of the employees are paid minimum wage

Question 8A sprinkler manufacturer claims that the average activating temperatures is at most 131 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p-value.

z-test statistic = 3.43, p-value = 0.0006

z-test statistic = -3.43, p-value = 0.0006

z-test statistic = -3.43, p-value = 0.0003

z-test statistic = 3.43, p-value = 0.0003

Question 9A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.8 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the population standard deviation is 2.3 seconds. Find the standardized test statistic and the corresponding p-value.

z-test statistic = -1.998, p-value = 0.023

z-test statistic = -1.998, p-value = 0.046

z-test statistic = 1.998, p-value = 0.046

z-test statistic = 1.998, p-value = 0.023

Question 10A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 41.5 milligrams.

Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic?

Claim is alternative, fail to reject the null and support claim as test statistic (2.05) is not in the rejection region defined by the critical value (1.64)

Claim is alternative, reject the null and support claim as test statistic (2.05) is in the rejection region defined by the critical value (1.64)

Claim is null, fail to reject the null and reject claim as test statistic (2.05) is not in the rejection region defined by the critical value (1.96)

Claim is null, reject the null and reject claim as test statistic (2.05) is in the rejection region defined by the critical value (1.96)

**APA Writing Checklist**

Use this document as a checklist for each paper you will write throughout your GCU graduate

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Check Out Also:** MATH 221: Statistics for Decision Making Week 6 Homework **

☐ APA paper template (located in the Student Success Center/Writing Center) is utilized for the correct format of the paper. APA style is applied, and format is correct throughout.

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☐ Topic is well defined.

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**Scholarly Resources: **Scholarly resources are written with a focus on a specific subject discipline and usually written by an expert in the same subject field. Scholarly resources are written for an academic audience.

**Examples of Scholarly Resources include:** Academic journals, books written by experts in a field, and formally published encyclopedias and dictionaries.

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**Empirical Journal Article**: This type of scholarly resource is a subset of scholarly articles that reports the original finding of an observational or experimental research study. Common aspects found within an empirical article include: literature review, methodology, results, and discussion.

Adapted from “Evaluating Resources: Defining Scholarly Resources,” located in *Research Guides* in the GCU Library.

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