The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard
Deviation of 0.5 ounces. At the .05 level of significance, perform a hypothesis test to see
If the true mean weight is less than 4 ounces.
The correct calculated value of the test statistic is
A) -0.4
B) 0.4
C) -1.55
D) 1.55
E) 2.79

Question

Quizplus · Accepted Answer

The null hypothesis is: H0: μ ≥ 4 (the true mean weight is greater than or equal to 4 ounces).
The alternative hypothesis is: Ha: μ < 4 (the true mean weight is less than 4 ounces).

Since the population standard deviation is not known and the sample size is small (n<30), we need to use a t-distribution to perform the hypothesis test. The degrees of freedom for this test is (n-1) = 14.

The calculated t-value can be found using the formula:
t = (x̄ - μ) / (s / √n)

Where x̄ is the sample mean, μ is the hypothesized population mean (4), s is the sample standard deviation, and n is the sample size.

t = (3.8 - 4) / (0.5 / √15) = -1.55

The corresponding critical t-value at the 0.05 level of significance with 14 degrees of freedom is -1.761. Since the calculated t-value (-1.55) is greater than the critical t-value (-1.761), we fail to reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the true mean weight of soy patties sold by Veggie Burgers Delight is less than 4 ounces at the 0.05 level of significance.

The correct answer is C (-1.55).

The Weights of Soy Patties Sold by Veggie Burgers Delight