A research report claims that 20 of all individuals use Fire

A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if the proportion of their users who use Firefox is significantly different from 0.2. In a sample of 200 of their users, 32 users stated that they used Firefox. Using this data, conduct the appropriate hypothesis test using a 0.05 level of significance.

a) What are the appropriate hypotheses?

A.)H₀: p = 0.2 versus H_a: p < 0.2

A.)H₀: p = 0.2 versus H_a: p 0.2    

C.)H₀: = 0.2 versus H_a: > 0.2

D.)H₀: p = 0.2 versus H_a: p > 0.2

b) What is the test statistic? Give your answer to four decimal places.  

c) What is the P-value for the test? Give your answer to four decimal places.  

d) What is the appropriate conclusion?

A.)Fail to reject the claim that the Firefox proportion is 0.2 because the P-value is larger than 0.05.

B.)Conclude that the Firefox proportion is not 0.2 because the P-value is larger than 0.05.    

C.)Fail to reject the claim that the Firefox proportion is 0.2 because the P-value is smaller than 0.05.

D.)Conclude that the Firefox proportion is not 0.2 because the P-value is smaller than 0.05.

Solution

a)

A.)H₀: p = 0.2 versus H_a: p ? 0.2    

b)

p = 32/200 = 0.16

z= 0.16 - 0.20   /   srqt(0.20*0.80 / 200 )

z= -0.04 / 0.02828   = -1.4142

c)

p value : 0.0793

d)

if p value is greater than significance level we fail to reject Ho

if p value is lower than significance level we reject Ho

A.)Fail to reject the claim that the Firefox proportion is 0.2 because the P-value is larger than 0.05.