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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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