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 H_a: 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.

He would not reject H₀ at a significance level of 0.05.

He would reject H₀ at a significance level of 0.05 but not at 0.025.

He would reject H₀ at a significance level of 0.025 but not at 0.01.

He would reject H₀ at a significance level of 0.01.

Answer 1

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (13.88 - 14) / 0.24 / $\sqrt$ 16

Test statistic = -2

df = 15

P-value = 0.032

He would reject H₀ at a significance level of 0.05 but not at 0.025