Question

A well-known brokerage firm executive claimed that 40% 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 700 people, 42% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 40% at the 0.025 significance level.

The null and alternative hypothesis would be:

H0:μ≥0.4H0:μ≥0.4
H1:μ<0.4H1:μ<0.4

H0:μ≤0.4H0:μ≤0.4
H1:μ>0.4H1:μ>0.4

H0:μ=0.4H0:μ=0.4
H1:μ≠0.4H1:μ≠0.4

H0:p≥0.4H0:p≥0.4
H1:p<0.4H1:p<0.4

H0:p=0.4H0:p=0.4
H1:p≠0.4H1:p≠0.4

H0:p≤0.4H0:p≤0.4
H1:p>0.4H1:p>0.4

The test is:

right-tailed

two-tailed

left-tailed

The test statistic is:  (to 3 decimals)

The p-value is:  (to 4 decimals)

Based on this we:

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

Answer 1

Null hypothesis  

                   
                      
Alternative hypothesis      

   

The test is:

right-tailed

           
                      
We have for given example,                      
Population proportion value is =0.4                  
x=294                  
                      
n=700                  
Level of significance =   0.025                  
Estimate for sample proportion
                      
Z test statistic formula for proportion

  
=1.080         

P value is = 0.1400................by using Z table or by using Excel command 1-NORMSDIST(1.080)

P value is =0.1400 > 0.025

Fail to reject the null hypothesis