Question

In: Statistics and Probability

A poll was taken this year asking college students if they considered themselves overweight. A similar...

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Let α = .05.

a)Formulate a hypothesis testing to test whether the proportion increased significantly (proportion of Sample 1 is greater than proportion of Sample 2).

b)What is the value of the test statistic?

c)What is the critical value of the test?

d)What is your conclusion? Explain it in the context of the problem.

Sample Size

Number Considered

Themselves Overweight
Present Sample (Sample 1) 300 150
Previous Sample (Sample 2) 275 121

Solutions

Expert Solution

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2


b)
p1cap = X1/N1 = 150/300 = 0.5
p2cap = X2/N2 = 121/275 = 0.44
pcap = (X1 + X2)/(N1 + N2) = (150+121)/(300+275) = 0.4713


Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5-0.44)/sqrt(0.4713*(1-0.4713)*(1/300 + 1/275))
z = 1.44

c)

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

d)

Fail to reject null hypothesis

There is not sufficient evidence to conclude that the proportion increased significantly (proportion of Sample 1 is greater than proportion of Sample 2).


orchestra answered 2 years ago
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