Question

Nutrition labels. The nutrition label on a bag of potato chips says that a serving of potato chips has 130 calories. A random sample of 58 bags yielded a sample mean of 134 calories with a standard deviation of 17 calories. Test the claim that the nutrition label on a bag of potato chips is correct.

(a) Write the hypotheses for the test:

• H_o: μ = 130
  H_a: μ > 134
• H_o: μ = 130
  H_a: μ ≠ 130
• H_o: μ = 130
  H_a: μ = 134
• H_o: σ = 17
  H_a: σ < 17

(b) Compute the p-value for the test:
p = (round to three sig figs)

(c) What is the final conclusion?

• There is not sufficient evidence to reject the claim that the true average calorie content is 130 calories.
• There is sufficient evidence to reject the claim that the true average calorie content is 130 calories.
• There is not sufficient evidence to support the claim that the true average calorie content is 130 calories.
• There is sufficient evidence to support the claim that the true average calorie content is 130 calories.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 130

H_a :    130

= 134

= 130

= 17

n = 58

Test statistic = z

= ( - ) / / n

= (134 - 130) / 17 / 58

= 1.79

Test statistic = 1.79

P(z > 1.79) = 1 - P(z < 1.79) = 1 - 0.9633 = 0.0367

P-value = 2 * 0.0367 = 0.0734

P-value = 0.073

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the claim that the true average calorie content is 130 calories.