Question

A sample of 103 mortgages approved during the current year showed that 45 were issued to a single-earner family or individual. The historical percentage is 37 percent.
  
At the .05 level of significance in a right-tailed test, has the percentage of single-earner or individual mortgages risen?

A) H₀: ππ ≤ .37 versus H₁: ππ > .37. Choose the right option. 1 or 2

1. Reject H₀ if z_calc > 1.645

2. Reject H₀ if z_calc < 1.645

A2) (a-2) Calculate the test statistic. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.)
  
Test statistic ______

B) (a-3) The null hypothesis should be rejected.
  

• True

• False

(b) Is this a close decision? Yes or No

C) (c) State any assumptions that are required.

n ππ < 10 and n(1 − ππ ) > 10

or

n ππ < 10 and n(1 − ππ ) < 10

or

n ππ > 10 and n(1 − ππ ) > 10

or

n ππ > 10 and n(1 − ππ ) < 10

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.37
Alternative Hypothesis, Ha: p > 0.37

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4369 - 0.37)/sqrt(0.37*(1-0.37)/103)
z = 1.4063

Fail to reject null hypothesis
False

No, not a close decision

assumptions: option C