Self-efficacy is a general concept that measures how well we think we can contro

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:

x

(a) Carry out the significance test using a one-sided alternative. Report the test statistic with the degrees of freedom and the P-value. (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.)

df=

P-value=

(e) 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.

(___,___)

x

Explanation / Answer

PART A.
Given that,
mean(x)=4.18
standard deviation , s.d1=1.19
number(n1)=165
y(mean)=3.65
standard deviation, s.d2 =1.12
number(n2)=218
null, Ho: u1 < u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.654
since our test is right-tailed
reject Ho, if to > 1.654
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =4.18-3.65/sqrt((1.4161/165)+(1.2544/218))
to =4.426
| to | =4.426
critical value
the value of |t | with min (n1-1, n2-1) i.e 164 d.f is 1.654
we got |to| = 4.42643 & | t | = 1.654
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 4.4264 ) = 0.00001
hence value of p0.05 > 0.00001,here we reject Ho
ANSWERS
---------------
null, Ho: u1 < u2
alternate, H1: u1 > u2
test statistic: 4.426
critical value: 1.654
decision: reject Ho
p-value: 0.00001

PART B.
given that,
mean(x)=4.18
standard deviation , s.d1=1.19
sample size, n1=165
y(mean)=3.65
standard deviation, s.d2 =1.12
sample size,n2 =218
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
where,
x1,x2 = mean of populations
sd1,sd2 = standard deviations
n1,n2 = size of both
a = 1 - (confidence Level/100)
ta/2 = t-table value
CI = confidence interval
CI = [( 4.18-3.65) ± t a/2 * sqrt((1.416/165)+(1.254/218)]
= [ (0.53) ± t a/2 * 0.12]
= [0.294 , 0.766]
-----------------------------------------------------------------------------------------------
interpretations:
1. we are 95% sure that the interval [0.294 , 0.766] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

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