Question

Consider the following hypothesis test H0 p 20 Ha p 20 A sample of 400 provided a sample proportion p 175 a Compute the value of the test statistic to 2 decimals 1.25 b What is the p value to 4 decimals 0.2113 c Using α 05 can you conclude that the population proportion is not equal to 20 Answer the next three questions using the critical value approach d Using α 05 what is the critical value for the test statistic to 2 decimals or 1.96 e State the rejection rule Reject H0 if z is

Answer 1

Answer:

a) -1.25

b) 0.2112

c) -1.96

Step-by-step explanation:

Data provided in the question:

Sample size, n = 400

H0 : p = 20

$\bar{p}$ = 175

Now,

a) The test statistic is  given as:

Z = $\frac{(\bar{p}-p)}{\sqrt{\frac{p(1-p)}{n}}}$

on substituting the respective values, we get

Z = $\frac{(0.175-0.2)}{\sqrt{\frac{0.2\times0.8}{400}}}$

= -1.25

b) The p-value = 2 × P(Z <-1.25)

Now from the standard normal table

P(Z <-1.25) = 10.56% = 0.1056

Thus,

p-value = 2 × 1056 = 0.2112

c) for a = 0.05,

the critical value is $Z_{\frac{a}{2}}=Z_{\frac{0.05}{2}}$ i.e $Z_{0.025}$

Now from standard normal table

$Z_{0.025}$ = -1.96