In 2011, a U.S. Census report determined that $71 %$ of college students work. A researcher thinks this percentage has changed since then. A survey of 110 college students reported that 91 of them work. Is there evidence to support the reasearcher's claim at the $1 %$ significance level? A normal probability plot indicates that the population is normally distributed.
a) Determine the null and alternative hypotheses.
$H_{0} : p =$
$H_{a} : p Select an answer v$
(Put in the correct symbol and value)
b) Determine the test statistic. Round to two decimals.
$z =$
c) Find the $p$ -value. Round to 4 decimals.
$P -value =$
d) Make a decision.
Fail to reject the null hypothesis
Reject the null hypothesis

Answer

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Answer

$H_{a} : p \neq 0.71$

Steps

Step 1 ：State the null and alternative hypotheses. The null hypothesis is that the proportion of college students who work is still 71%, or 0.71. The alternative hypothesis is that the proportion has changed, which means it could be either less than or greater than 0.71. Therefore, this is a two-tailed test.

Step 2 ： $H_{0} : p = 0.71$

Step 3 ： $H_{a} : p \neq 0.71$

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