Question

Inference for comparing two means

1. In a study for effect of diet and exercise on weight loss, we consider two randomly selected groups and the following table showing weight loss on average and its standard deviation. Assume these two group are independent. (30 points)

30 days results
Just Diet (JD)	2.3lb	1.5 lb	28
Diet Plus Exercise (DPE)	3.5lb	1.1lb	30

1. Write the null hypothesis and alternative hypothesis.
2. Find the test statistics.
3. If  Can you reject the null hypothesis?

Answer 1

(a) The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

(b) The test statistic is -3.491.

(c) The p-value is 0.0009.

Since the p-value (0.0009) is less than the significance level (0.05), we can reject the null hypothesis.

JD	DPE
2.3	3.5	mean
1.5	1.1	std. dev.
28	30	n
	56	df
	-1.2000	difference (JD - DPE)
	1.7114	pooled variance
	1.3082	pooled std. dev.
	0.3438	standard error of difference
	0	hypothesized difference
	-3.491	t
	.0009	p-value (two-tailed)