Question

A research group wants to estimate the proportion of Americans who can speak a language other than English. By referencing past data the group believes that more than 45% of Americans can do so.

a. state the nulled alternate hypothesis for the group's belief.

b. if the value of the test statistic is approximately 1.46, what is the conclusion (reject H0 or fail to reject H0) of the hypothesis test? with x = 0.05

c. if the true value is 48%, did the researchers make an error? If so, what type?

Answer 1

a. Here claim is that p>0.45

So hypothesis is vs

b. Test statistics is z=1.46, so P value is

Hence we fail to reject the null hypothesis

c. Here actual p=0.48 so claim is correct hence we need to reject null hypothesis. But we have failed to reject the null hypothesis

Hence it is Type II error, as Type II error is failing to reject the false null hypothesis

answered by: anonymous