A new diet program claims that participants will lose on average at least eight

Question

A new diet program claims that participants will lose on average at least eight pounds during the first week of the program. A random sample of 40 people participating in the program showed a sample mean weight loss of seven pounds. The sample standard deviation was 3.2 pounds. Using a 0.1 significance level, test whether there is sufficient evidence to reject the claim of a mean weight loss of at least 8 pounds.

a. Clearly state your null and alternative hypothesis and determine this is a one-tailed or two-tailed test.

b. Find sample mean, sample standard deviation and calculate standard error.

c. Compute z-score and corresponding p-value. Explain the meaning of this p-value.

d. Draw your conclusion on whether there is sufficient evidence to reject the claim of a mean weight loss of at least 8 pounds.

Explanation / Answer

Ho : Weight loss >= 8 pounds

Ha : Weight loss < 8 pounds

Since,an inequality is involved, it is a one tailed test.

Sample mean = 7 pounds

Stdev. = 3.2 pounds

S.E = s / sqrt(n)

= 3.2 / sqrt ( 40 )

= 0.5059

z -score : = 7 - 8 / 0.5059

= -1.9764

p - value = 0.024077

which means the null hypothesis is rejected

So, it is insufficient to draw the conclusion that the weight loss is more than 8 pounds

Hope this helps.

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