Question

It is believed that the average amount of money spent per U.S. household per week on food is about $96, with standard deviation $9. A random sample of 49 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.

a) H_o: μ = 96, H_a: μ ≠ 96; z = -3.111; Yes, we should reject H_o.

b) H_o: μ = 96, H_a: μ > 96; z = 3.111; No, we should fail to reject H_o.

c) H_o: μ = 96, H_a: μ > 96; z = 3.111; Yes, we should reject H_o.

d) H_o: μ = 96, H_a: μ < 96; z = -0.311; No, we should fail to reject H_o.

e) H_o: μ = 96, H_a: μ ≠ 96; z = 0.311; Yes, we should reject H_o.

Answer 1

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : $\mu$ = 96

H_a : $\mu$ > 96

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$    / $\sqrt$ n

= (100 - 96) / 9 / $\sqrt$ 49

= 3.111

Test statistic = 3.111

P-value = 0.0009

P-value < $\alpha$

Reject the null hypothesis .

c) H_o: μ = 96, H_a: μ > 96; z = 3.111; Yes, we should reject H_o.