Question

A researcher reports that 14% of the population is left-handed. In a recent random sample of 300 people, 45 were left-handed. Test the researcher's claim at alpha = 0.05 using the p-value method. a) What type of hypothesis test is this? b) What is the correct TV? c) What is the correct p-value? d) What is the correct summary for this problem?

Answer 1

a) What type of hypothesis test is this?

This is a z test for population proportion.

b) What is the correct TV?

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 45

n = sample size = 300

p̂ = x/n = 45/300 = 0.15

p = 0.14

q = 1 - p = 0.86

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.15 – 0.14)/sqrt(0.14*0.86/300)

Z = 0.4992

Test statistic = 0.4992

c) What is the correct p-value?

P-value = 0.6177

(by using z-table)

d) What is the correct summary for this problem?

P-value > α = 0.05

So, we do not reject the null hypothesis at 5% level of significance.

There is sufficient evidence to conclude that that 14% of the population is left-handed.