Question

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. 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, 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 oz with a standard deviation of s = 0.24 oz.  

What is the value of the test statistic?

Select one:

a. t=-8.55

b. t=-0.10

c. t=-0.75

d. t=-2.00

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. 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, 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 oz with a standard deviation of s = 0.24 oz.  

Determine which of the following statements regarding the decision the representative would make is true:

Select one:

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

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

c. He would reject H₀ at a significance level of 0.01.

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

Answer 1

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Hypothesis: VS

The test statistic is ,

The critical value is ,

; The Excel function is , =TDIST(2,15,1)

Decision : If p-value < significance level= , then reject Ho , accept otherwise.

Here ,

a. For =0.05

Decision : p-value=0.032<=0.05

Therefore , reject Ho.

b. For =0.025

Decision ; p-value=0.032>=0.025

Therefore , fail to reject Ho

c. For =0.01

Decision ; p-value=0.032>=0.01

Therefore , fail to reject Ho

Correct option : (b) He would reject H0 at a significance level of 0.05 but not at 0.025.