*For this problem (use excel for descriptives, but calculate t-statistic and p v
ID: 3200936 • Letter: #
Question
*For this problem (use excel for descriptives, but calculate t-statistic and p values by hand).
-To investigate an alleged unfair trade practice, the Federal Trade Commission (FTC) takes a random sample of 16 "5-ounces" candy bars from a large shipment. the mean of the sample weights is 4.85 ounces and the sample standard deviation is 0.1 ounce.Test the hypotheses: H0: u greater or equal 5 and Ha: u <5 at the 5% level of significance. Assume the population of candy bar weights is approximately normally distributed. Based on the results of the test, does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling? State the decision rule, the test statistic, and your decision. Thanks
.*Note: I deeply apologize. Yes, you were right i forgot the standard deviation which is 0.1 ounces. i just correct it. Thank you.
Explanation / Answer
Null hypothesis: >= 5
Alternative hypothesis: < 5
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Decision rule: P value < 0.05
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), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
= 0.1 / sqrt(16)
= 0.025
DF = n - 1 = 16 - 1 = 15
t = (x - ) / SE
= (4.85 - 5)/0.025
= -6
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.
Now, we need to find p value byusing t satistic value and degree of freedom
So, p value = .000012.
So, p value , 0.05 It means we reject the null hypothesis.
Yes,FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling
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