Question

Can ypu show the formula you used and how you worked out the prpblem?

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:

a=

Decision Rule:

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

Conclusion:

Answer 1

We want to test whether the true proportion of the population that believes Elvis Presley is still alive is less than 10%.The hypotheses are :

H0 : p = 0.1

H1 : p < 0.1

Here, n = 1248 and the sample proportion , = 8 % = 0.08

alpha = 0.01

The test statistic , z = ( - p) / {p(1-p)/n}

= -0.02 / 0.0085

= -2.35

At alpha 0.01 , z(critical) = -2.33

Therefore, decision rule is reject H0 if z < -2.33.

Here, z = -2.35 and hence,z < z(critical). We reject the null hypothesis at alpha = 0.01.

We conclude that the true proportion of the population that believes Elvis Presley is still alive is less than 10%.