Question

Self-efficacy is a general concept that measures how well we think we can control different situations. A multimedia program designed to improve dietary behavior among low-income women was evaluated by comparing women who were randomly assigned to intervention and control groups. Participants were asked, "How sure are you that you can eat foods low in fat over the next month?" The response was measured on a five-point scale with 1 corresponding to "not sure at all" and 5 corresponding to "very sure." Here is a summary of the self-efficacy scores obtained about 2 months after the intervention:

Group	n	x	s
Intervention	169	4.12	1.19
Control	217	3.65	1.12

Carry out the significance test using a one-sided alternative. Report the test statistic with the degrees of freedom and the P-value. (Use μ_Intervention − μ_Control. Round your test statistic to three decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal places.)

t=

df=

P-value=

Find a 95% confidence interval for the difference between the two means. Compare the information given by the interval with the information given by the significance test.

(    ,    )

Answer 1

H₀:

H₁:

t = ()/sqrt(s1^2/n1 + s2^2/n2)

= (4.12 - 3.65)/sqrt((1.19)^2/169 + (1.12)^2/217)

= 3.950

df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

    = ((1.19)^2/169 + (1.12)^2/217)^2/(((1.19)^2/169)^2/168 + ((1.12)^2/217)^2/216)

    = 350

P-value = P(T > 3.950)

             = 1 - P(T < 3.950)

             = 1 - 1 = 0

At alpha = 0.05, Since the P-value is less than the significance level(0 < 0.05), so we should reject H₀.

At 95% confidence interval the critical value is t^* = 1.967

The 95% confidence interval for is

() +/- t^* * sqrt(s1^2/n1 + s2^2/n2)

= (4.12 - 3.65) +/- 1.967 * sqrt((1.19)^2/169 + (1.12)^2/217)

= 0.47 +/- 0.234

= 0.236, 0.704

Since confidence interval doesn't contain 0, so we should reject H₀.