Answer :
Final answer:
To test the claim of the Mars Candy Company, we can perform a hypothesis test by comparing the observed proportion of brown M&M's in the sample to the claimed proportion. The test statistic value can be calculated using the formula: Z = (p - P) / sqrt((P(1-P))/n). The result of the hypothesis test can be determined by comparing the test statistic to the critical value.
Explanation:
To test the claim of the Mars Candy Company, we can perform a hypothesis test by comparing the observed proportion of brown M&M's in the sample to the claimed proportion. Let's perform a one-sample proportion test using a significance level of 0.05.
A. The test statistic value can be calculated using the formula: Z = (p - P) / sqrt((P(1-P))/n). In this case, the observed proportion is 8% or 0.08, and the claimed proportion is 13% or 0.13. Using the provided sample size of 100, we can plug these values into the formula to calculate the test statistic.
B. The critical value depends on the significance level and the type of test. Since we are performing a one-tailed test in this case, the critical value is the z-score corresponding to the 0.05 significance level in the lower tail of the standard normal distribution. We can use a standard normal distribution table or a calculator to find this value.
C. To determine the result of the hypothesis test, we compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis (claim of Mars Candy Company) and conclude that there is evidence to suggest that the proportion of brown M&M's is different from what the company claims. If the test statistic is less than the critical value, we fail to reject the null hypothesis and do not have enough evidence to conclude that the proportion is different.
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