Question

1. Egg Beaters are egg substitutes with no fat or cholesterol but with the same amount of protein as a regular egg (6 grams). In order to check the protein claim, 18 Egg Beaters were randomly selected and the amount of protein in each was measured. The sample mean is 6.07 grams. Is there any evidence to suggest the mean amount of protein in an Egg Beater is different from the amount of protein in a regular egg? Assume the mean amount of protein in Egg Beater is normally distributed, σ=0.6 grams, and α=0.0

1. State the null and alternative hypotheses.
2. Find the test statistic.
3. Find the P-value.
4. State the conclusion of the test (reject null hypothesis or fail to reject null hypothesis).
5. Interpret the conclusion in context.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 6

H_a :    6

= 6.07

= 6

= 0.6

n = 18

Test statistic = z

= ( - ) / / n

= (6.07 - 6) / 0.6 / 18

= 0.495

Test statistic = 0.495

P(z > 0.495) = 1 - P(z < 0.495) = 1 - 0.6897 = 0.3103

P-value = 2 * 0.3103 = 0.6206

= 0.05  

P-value >

Fail to reject the null hypothesis .

There is no sufficient evidence to suggest that the mean amount of protein in an Egg Beater is

different from the amount of protein in a regular egg .