Question

A study was conducted to determine the proportion of "regular" online customers. In a sample of 100 people, 60 people declared that they make online purchases regularly. It is claimed that more than 50% are "regular" online customers.

What is the parameter of interest and the type of test associated with the hypothesis test testing the validity of the above claim?

μμ and left tailed

p and right tailed

μμ and right tailed

p and two tailed

p and left tailed

Calculate the appropriate test statistic, correct up to 3 decimal places.

State the critical value(s) associated with a significance level of .01

Calculate the minimum sample size to compute a 99% confidence interval of the true proportion of regular online customers within .01

Answer 1

1)

n=100, x=60, P= 50%= 0.50, = 0.01

a)

Ho: p 0.50

Ha: p > 0.50

p and right tailed

b)

z = 2.000

Test statistics = 2.000

c)

now find z critical value for right tailed test with  = 0.01

using normal ztable we get

Critical value =2.326

d)

since (Test statistics = 2.000 ) < ( Critical value =2.326)

Failed to reject the null hypothesis.

Therefore there is not sufficient evidence to support the claim that more than 50% are regular online customers.

2)

c= 99%, E= 0.01

formula for sample size is

Where Zc is the z critical value for c=99%

Zc = 2.576

n =16589.44

minimum sample size required = 16590