Chapter PV, Problem 35RE

To determine

To explain what do you think about the statement made.

Answer to Problem 35RE

There is sufficient evidence that Bush had a lower disapproval rating.

Explanation of Solution

It is given in the question that pundits started discussing whether his rating was still discernibly better than Nixon’s. Let us first check the conditions as,

Random condition: It is satisfied as the sample was randomly selected from the population.

Independent condition: It is satisfied as we can assume that the sample is independent.

  $10\%$ condition: It is satisfied as the sample is less than $10\%$ of all African-American women.

Success/failure condition: It is satisfied because both are greater than ten as,

  $\begin{array}{l}np=630>10\\ n(1-p)=370>10\end{array}$

Thus, all the conditions are satisfied. Thus, to calculate an appropriate hypothesis we will use $\text{TI}-89$ calculator. Thus, for this first we have to select $5:1-\text{PropZInt}$ from the STAT TESTS menu. Then, enter the observed counts and sample sizes for both the samples. Then we will indicate what kind of test we want: one-tail lower tail, two-tail, or one-tail upper tail. Then, we will specify whether to calculate the result or draw the result. Hence we have,

  $\begin{array}{l}x=630\\ n=1000\\ c=0.95=95\%\\ H_0:p=0\\ H_a:p<0\end{array}$

So, by putting the values above by using the calculator we will get the result as,

The P-value will be then,

  $P=0.0226$

And as we know if the P-value is smaller than the significance level, then reject the null hypothesis, so, we have,

  $P<0.05\Rightarrow \text{ Reject }{H}_0$

Thus, we conclude that there is sufficient evidence that Bush had a lower disapproval rating.