Chocolate bars produced by a certain machine are labeled 8.0 oz. The distributio

Question

Chocolate bars produced by a certain machine are labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be normal. A quality control team checked a sample of 30 chocolates and found their average weight to be 7.85 oz and their standard deviation 0.1 oz.

1.At the level of significance of 5%, what is this conclusion?

2.What would it mean to make a Type I Error in this context? What does it mean to make a Type II error in this context?

3. What is the probability the economist will make a type I error?

4. What type of error could he have made at this level of significance?

5. Give an example of a level of significance for which we will not reject the null and one where we will reject it?

Explanation / Answer

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 8.0
Alternative hypothesis: 8.0

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.01826

z = (x - ) / SE

z = - 8.22

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than - 8.22 or greater than 8.22.

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

2) Type I error - In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis.

Type II error - Type II error is incorrectly retaining a false null hypothesis.

3) The probability the economist will make a type I error is 0.05.

4) The type of error could he have made at this level of significance is type I error.

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