Question

ags 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 and are Normally distributed with mean μ. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised so he intends to test the following hypotheses: H0: μ = 14, Ha: μ < 14 To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the sample mean to be = 13.88 and the sample standard deviation to be s = 0.24. Reference: Ref 7-4 Suppose in a similar test of 16 bags of these tortilla chips the test statistic has the value –2.126. In that case, we would reject H0 at significance level:

A.0.01

B.0.05 but not 0.025

C.0.025 but not at 0.01

D.0.1 but not at 0.05

Please show work THX!

Answer 1

Solution:

We have to test the hypothesis

H0: μ = 14, Ha: μ < 14

For testing this , a sample of size n = 16 is taken

Suppose in a similar test of 16 bags of these tortilla chips the test statistic has the value –2.126.

t = -2.126

Observe that , there is < sign in the alternative hypothesis Ha

So , LEFT Tailed Test.(One tailed left sided )

Degrees of freedom = n - 1 = 16 - 1 = 15

Now , go to t distribution table.

Go to 15 d.f.

Observe where the value |-2.126| = 2.126 fits (In the one tailed)

So , range of the p value is " 0.025 < p value < 0.05

When the p value is less than the significance level , we reject the null hypothesis H₀

Otherwise , we fail to reject null hypothesis H₀

So , answer is

B.0.05 but not 0.025