Please show all work and formulas used and dont use excel or

Please show all work and formulas used and don\'t use excel or similar program. Thank you!

Consider the hypothesis test given by

H₀: p=0.5

H₁:p>0.5

In a random sample of 100 subjects, the sample proportion is found to be p^= 0.55

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P -value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of H₀at the a=0.01 level? Explain.

Solution

H₀: p=0.5

H₁:p>0.5

This is right tailed test for proportions

As n =100, >30 z test can be used

p difference = 0.55-0.5 = 0.05

Std error = 0.05

The two samples are not significantly different.

As p value >0.01 there is no sufficient evidence to justify the rejection of H₀ at the a=0.01 level