9. Hypothesis Testing for One Sample

Student loan debt has fluctuated over years, with signs indicating that the default rate may be increasing. Write the null and alternative hypothesis if you want to determine if the student loan default rate this year is more than $15\%$.

A transportation analyst claims that the average commute time in a major city is less than $45$ minutes. A hypothesis test is conducted, with a resulting P-value of $0.0084$. What would be the conclusion at a significance level $\alpha =.01$

A survey claimed that $30\%$ of adults prefer electric cars over traditional cars. A car manufacturer believes the true proportion is higher than $30\%$. To test this, they survey a random sample of $50$ adults and find that $19$ say they prefer electric cars. Determine which test statistic to use & calculate it.

A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than $0.300$ g. Write the null and alternative hypotheses.

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

$H_0:$ $p=0.4$

$H_{a}:$ $p\(\ne\)0.4$

A popular theme park claims that their weekly attendance is around $100,000$. You believe that the weekly attendance is different than this claimed value, so you gather sample data. Write the null and alternative hypotheses.

In a certain hypothesis test, $H_0:p=0.4$, $H_{a}:p$ < $0.4$. You collect a sample and calculate a test statistic $z=-1.32$. Find the $P$-value.