Question

Our teacher has us suing the Geogebra Statistic calculator -

Hypothesis Test for a Population Proportion

A well-known brokerage firm executive claimed that 70% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 400 people, 68% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 70% at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:p≤0.7H0:p≤0.7
H1:p>0.7H1:p>0.7

H0:μ≥0.7H0:μ≥0.7
H1:μ<0.7H1:μ<0.7

H0:μ≤0.7H0:μ≤0.7
H1:μ>0.7H1:μ>0.7

H0:μ=0.7H0:μ=0.7
H1:μ≠0.7H1:μ≠0.7

H0:p=0.7H0:p=0.7
H1:p≠0.7H1:p≠0.7

H0:p≥0.7H0:p≥0.7
H1:p<0.7H1:p<0.7

The test is:

right-tailed

left-tailed

two-tailed

The test statistic is:  (to 3 decimals)

The p-value is: (to 4 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Answer 1

Solution :

Given that,

= 0.70

1 - = 0.30

n = 400

Level of significance = = 0.05

Point estimate = sample proportion = = 0.68

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.70

Ha: p < 0.70

Test statistics

z = ( - ) / *(1-) / n

= ( 0.68 - 0.70) / (0.70*0.30) / 400

= -0.873

P-value = P(Z < z )

= P(Z < -0.87 )

= 0.8087

The p-value is p = 0.8087, and since p = 0.8087 > 0.05, it is concluded that fail to reject the null hypothesis.

Fail to reject the null hypothesis.