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Testing Claims About Proportions. In Exercises 9鈥32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

M&Ms Data Set 27 鈥淢&M Weights鈥 in Appendix B lists data from 100 M&Ms, and 27% of them are blue. The Mars candy company claims that the percentage of blue M&Ms is equal to 24%. Use a 0.05 significance level to test that claim. Should the Mars company take corrective action?

Short Answer

Expert verified

Nullhypothesis: The proportion of blue M&Ms is equal to 0.24.

Alternativehypothesis: The proportion of blue M&Ms is not equal to 0.24.

Teststatistic: 0.702

Criticalvalue: 1.96

P-value: 0.4827

The null hypothesis is failed to reject.

There is not enough evidence to reject the claim that the proportion of blue M&Ms is equal to 0.24.

Since the proportion of blue M&Ms is equal to 24% per the claim of the company, the company does not need to take any corrective measure.

Step by step solution

01

Given information

The proportion of blue M&Ms in a sample of 100 M&Ms is equal to 27%.

02

Hypotheses

The null hypothesis is written as follows:

The proportion of blue M&Ms is equal to 24%.

H0:p=0.24

The alternative hypothesis is written as follows:

The proportion of blue M&Ms is not equal to 24%.

H1:p0.24

The test is two-tailed.

03

Sample size, sample proportion, and population proportion

The sample size is equal to n=100.

The sample proportion of blue M&Ms isas follows:

p^=27%=27100=0.27

The population proportion of blue M&Ms is equal to 0.27.

04

Test statistic

The value of the test statistic is computed below:

z=p^-ppqn=0.27-0.240.241-0.24100=0.702

Thus, z=0.702.

05

Critical value and p-value

Referring to the standard normal distribution table, the critical value of z at =0.05 for a two-tailed test is equal to 1.96.

Referring to the standard normal distribution table, the p-value for the test statistic value of 2.694 is equal to 0.4827.

Since the p-value is greater than 0.05, the null hypothesis is failed to reject.

06

Conclusion of the test

There is not enough evidence to reject the claim that the proportion of blue M&Ms is equal to 0.24.

Since the proportion of blue M&Ms is equal to 24% per the claim of the company, the company does not need to take any corrective measure.

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Most popular questions from this chapter

Final Conclusions. In Exercises 25鈥28, use a significance level of = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.

Test Statistics. In Exercises 13鈥16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)

16. Exercise 8 鈥淧ulse Rates鈥

Testing Claims About Proportions. In Exercises 9鈥32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Bias in Jury SelectionIn the case of Casteneda v. Partida,it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use a 0.01 significance level to test the claim that the selection process is biased against Americans of Mexican ancestry. Does the jury selection system appear to be biased?

Final Conclusions. In Exercises 25鈥28, use a significance level of = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.

P-Values. In Exercises 17鈥20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = -1.94 is obtained when testing the claim that p=38 .

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