Question

USA Today ran a report about a University of North Carolina poll of 1248 people from the southern

United States, in which they were asked if they believe that Elvis Presley is still alive. At the 0.01 level,

test the claim that the true proportion of the population that believes Elvis Presley is still alive is less than

10%.

H0:

H1:

=

Decision Rule:

8% of those interviewed believe that Elvis is still alive.

Test:

Conclusion:

Answer 1

USA Today ran a report about a University of North Carolina poll of 1248 people from the southern

United States, in which they were asked if they believe that Elvis Presley is still alive. Hence the sample size is N = 1248

and 8% of those interviewed believe that Elvis is still alive hence the sample proportion is = 0.08

Given the the claim that the true proportion of the population that believes Elvis Presley is still alive is less than 10%, hence the population proportion is p = 0.10.

Based on the claim the hypotheses are:

Based on the hypothesis it will be left tailed test, since the sample size is greater than 30 and the requirement for assuming that the distribution is normal is n*p*(1-p) >=10, so, 1248*0.10*(1-0.10) = 112.32 which is greater than 10 hence requirement is satisfied so, Z statistic is applicable for hypothesis testing.

Decision rule:

Given the significance level is 0.01 and based on the type of hypothesis the critical score for rejection region is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.01), thus the Zc computed as -2.33.

No reject the Ho if Z< -2.33 or P-value is less than 0.01

Test statistic:

The test statistic is calculated as:

Where po = 0.10 and qo = 1-0.10 = 0.90 thus the Zc is computed as -2.355

P-value:

The P-value is computed uisng the excel formula for normal distribution which is =NORM.S.DIST(-2.355, TRUE), thus the P-value is computed as 0.0094.

Conclusion:

Since the P-value is less than 0.01 and Z < Zc hence we reject the null hypothesis and conclude that there is enough evidence to support the claim that the population that believes Elvis Presley is still alive is less than10%.