Question

10. A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting news. A random sample of 88 urban residents showed that 12 subscribed. A random sample of 97 suburban residents showed that 18 subscribed. Does this indicate that there is a difference in the proportion of suburban residents that subscribe to this magazine? Use alpha at .05. a. State the null and alternative hypotheses (.5 points) b. What is the formula you will use? (.5 points) c. Identify all variables and corresponding values from the formula. Calculate the test statistic. (2 points) d. Sketch the distribution, label the critical value(s), shade the critical region(s), and plot the calculated test statistic. (1.5 points) e. Interpret your result. (1.5 points)  

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 12 + 18 ) / ( 88 + 97 )
= 0.1622
= 1 - = 0.8378
Z = -0.91

Test Criteria :-
Reject null hypothesis if

= -0.91 > -1.96, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z > -0.91 )
P value = 0.36
Reject null hypothesis if P value <
Since P value = 0.36 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that   the proportion of suburban residents that subscribe to this magazine use 5% level of significance.