Use the following to answer the question(s) below.
The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 108 grams with a sample standard deviation of 14 grams. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 113 grams.
-The correct calculated value of the test statistic is
A) -0.4
B) 0.4
C) -1.38
D) 1.38
E) 2.79

Question

Quizplus · Accepted Answer

The test statistic can be calculated as: 
t = (x̄ - μ)/(s/√n) 
where x̄ is the sample mean, μ is the hypothesized population mean (113 grams in this case), s is the sample standard deviation, and n is the sample size.

Substituting the given values: 
t = (108 - 113)/(14/√15) 
t = -1.38

Looking up the t-distribution table with 14 degrees of freedom (df = n - 1 = 15 - 1), at the 0.05 level of significance and for a left-tailed test (since the alternative hypothesis is less than), the critical value is -1.761.

Since the calculated value of t (-1.38) is greater than the critical value (-1.761), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the true mean weight is less than 113 grams.

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