Question

Given ˆpp^ = 0.3714 and N = 35 for the high income group,

Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.1 significance level.

a) Identify the correct alternative hypothesis:

• μ>.50μ>.50
• p=.50p=.50
• p<.50p<.50
• p>.50p>.50
• μ=.50μ=.50
• μ<.50μ<.50

Give all answers correct to 3 decimal places.

b) The test statistic value is:     

c) Using the P-value method, the P-value is:  

d) Based on this, we

• Reject H0H0
• Fail to reject H0H0

e) Which means

• The sample data supports the claim
• There is sufficient evidence to warrant rejection of the claim
• There is not sufficient evidence to support the claim
• There is not sufficient evidence to warrant rejection of the claim

Answer 1

Solution:

Given:

p^ = 0.3714 and N = 35 for the high income group,

Claim:  the proportion of children in the high income group that drew the nickel too large is smaller than 50%.

significance level = 0.1

Part a) Identify the correct alternative hypothesis:

Claim is directional to left side, thus this is left tailed test.

Thus

H1: p < 0.50

Part b) The test statistic value is:

Part c) Using the P-value method, the P-value is:  

P-value = P( Z< -1.522 )

Use following Excel command to get P-value:

=NORM.S.DIST(z,cumulative)

=NORM.S.DIST(-1.522,TRUE)

=0.064

Thus

P-value = 0.064

Part d) Based on this, we:

Decision Rule:
Reject null hypothesis H0, if P-value < 0.10 level of significance, otherwise we fail to reject H0
Since P-value = 0.064 < 0.10 level of significance, we reject null hypothesis H0.

Thus correct answer is: Reject H0

Part e) Which means

The sample data supports the claim