Question

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag. Assume net weights are Normally distributed. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0: μ = 14 versus Ha: μ < 14. To do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. He finds a sample mean of 13.88 ounces with a standard deviation of s = 0.24 ounces. Determine which of the following statements is true, regarding the decision the representative would make.

a.) He would reject H0 at a significance level of 0.05 but not at 0.025.
b.) He would reject H0 at a significance level of 0.025 but not at 0.01.
c.) He would not reject H0 at a significance level of 0.05.
d.) He would reject H0 at a significance level of 0.01.

Answer 1

Answer: A

Explanation:

Since the standard deviation of the population is unknown, a t-distribution must be used

`t=(x_(bar)-u_o )/((s)/(√(n) ) ) \\\\t=(13.88-14)/((0.24)/(√(16) ) ) = -2\\d.f=n-1=15\\P(t<-2) \ at\ 15\ d.f\\calculator...\\ p-value = 0.03197\\A) True\\Others are False`