In Exercises 1–10, use the following weights (g) of Hershey’s ...

Question

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

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tTest The bag of Hershey’s Kisses includes 75 of the candies. According to the label, the total weight is 340 g, so the candies should have a mean weight of 340/75 = 4.5333 g. Use the sample of weights listed above to test the claim that they are from a population with a mean of 4.5333 g. Use a 0.05 significance level with a t test. What does the conclusion suggest about the claim of 340 g printed on the label?

Accepted Answer

Hello, everyone, let's take a look at this question together. A company claims that the average weight of its chocolate truffles is 8.25 g. A quality control inspector randomly selects 10 truffles and records their weights in grams. And here we have the weights of the 10 truffles in grams. At the 0.05 significance level, use the T test to test the claim that the sample of weights. is from a population with a mean of 8.25 g. And so the first step in solving this problem is to state the hypotheses where our null hypothesis is that the population mean is mu equals 8.25 g, and our alternative hypothesis is that the population mean is not mu equals 8.25 g. And so our next step is to calculate the sample mean and the standard deviation which using the data that we are provided, we can compute the rest of the values in the table, which we can see that our sample mean of X bar is 8.255 and our standard deviation is 0.0525. And using the values for the sample mean and the standard deviation, we can calculate. the T statistic using the formula for the T statistic, which is T equals X minus mu divided by S divided by the square root of N, which substituting the values into the T statistic formula, our T statistic is approximately 0.301. And now we can determine the degrees of freedom and the critical T value, which our degrees of freedom is equal to N minus. 1, so our degrees of freedom is 9, and for a 2 tail test an alpha equals 0.05 using a T table, the T critical value is approximately 2.262. And now we can compare the calculated T value to the critical value, and since 0.301 is less than 2.262, we fail to reject the null hypothesis. Therefore, at the 0.05 significance level, there is insufficient evidence to support the claim that the population mean weight is not 8.25 g. So answer choice B is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

t-Test

Significance Level

Null Hypothesis

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