Question

(Round all intermediate calculations to at least 4 decimal places.)

An advertisement for a popular weight loss clinic suggests that participants in its new diet program lose, on average, more than 9 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 17 women who recently joined the weight reduction program. She calculates the mean weight loss of these participants as 10.6 pounds with a standard deviation of 2.7 pounds. Use Table 2.

a.

Set up the competing hypotheses to test the advertisement’s claim.

	H0: μ = 9; HA: μ ≠ 9
	H0: μ ≥ 9; HA: μ < 9
	H0: μ ≤ 9; HA: μ > 9

b.	At the 5% significance level, specify the critical value. (Round your answer to 3 decimal places.)

Critical value

c.	Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

d.	What does the consumer activist conclude?

(Click to select)Do not rejectReject H0. The claim by the weight loss clinic (Click to select)is notis supported by the sample data.

Answer 1

a)

H0: <= 9 , Ha: > 9

b)

df = n-1 = 17-1 = 16

t critical value at 0.05 level with 16 df = -1.746

c)

Test statistics

t = - / S / sqrt(n)

= 10.6 - 9 / 2.7 / sqrt(17)

= 2.44

d)

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

Reject H0. Claim by weight loss clinic is supported by sample data.