In: Statistics and Probability
Use the following to answer all of the questions. According to the Pew Internet and American Life Project 75% of American adults use the Internet. A survey of 600 adults aged 50-64 found 420 used the Internet (70%). We want to determine whether the proportion of Internet users age 50-64 differs from the overall proportion of 0.75. 1.What is the alternative hypothesis?
2. Compute the test statistic. Give answer to two decimal places.
3. Compute the p-value. Round answer to four decimal places.
4. If a=.05, what is the conclusion to the test? Reject Ho or Do not Reject Ho
The provided details are:
n=600 sample size, no of favorable condition X=420 hence sample proportion is :
The Hypotheses are:
Based on the given hypothesis it will be a two-tailed Z test
1) The test statistic:
2) P-value :
P-value is computed using the Z table or excel tool as:
P-value=0.0047
3) Rejection region:
At 0.05 level of significance reject Ho if |Z| >Z 0.025 =1.96 Computed using the Z table shown below with illustration.
Conclusion:
Since P-value <0.05 hence we reject the Null hypothesis and conclude that there is sufficient evidence to support the claim.
Z table: