Question

1) A well-known brokerage firm executive claimed that 30% 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 300 people, 34% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 30% at the 0.10 significance level.

a) The null and alternative hypothesis would be:

H0:p≤0.3
H1:p>0.3

H0:p=0.3
H1:p≠0.3

H0:μ≥0.3
H1:μ<0.3

H0:μ≤0.3
H1:μ>0.3

H0:p≥0.3
H1:p<0.3

H0:μ=0.3
H1:μ≠0.3

2) The test is:

a) The test statistic is: _______ (to 3 decimals)

b) The p-value is: ________ (to 4 decimals)

c) Based on this we:

Reject the null hypothesis

or

fail to reject the null hypothesis

Answer 1

H0:p≤0.3
H1:p>0.3

2) Z Hypothesis test for one proportion              

a)

Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.3400                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.02646                  
Z Test Statistic = ( p̂-p)/SE = (   0.3400   -   0.3   ) /   0.0265   =   1.512

b) p-Value   =   0.0653
c) Decision:   p-value<α , reject the null hypothesis