Question

A nutritionist claims that the mean tuna consumption by a person is 3.5 pounds per year. A sample of 90 people shows that the mean tuna consumption by a person is 3.4 pounds per year. Assume the population standard deviation is 1.04 pounds. At alphaequals0.02​, can you reject the​ claim? ​(a) Identify the null hypothesis and alternative hypothesis.

Answer 1

Claim: mean tuna consumption by a person is 3.5 pounds per year.

The null and alternative hypothesis are

H0: = 3.5

Ha: 3.5

Test statistics

z = - / / sqrt(n) .

= 3.4 - 3.5 / 1.04 / sqrt(90)

= -0.91

This is test statistics value.

Critical value at 0.02 level = -2.326, 2.326

Since test statistics falls in non-rejection region, we do not have sufficient evidence to reject H0.

p-value = 2 * P( Z <z)

= 2 * P( Z < -0.91)

= 2 * 0.1814

= 0.3628

We conclude at 0.02 level that we fail to support the claim.