A manufacturer produces bottles of olive oil labelled as containing $500\text{ mL}$. A quality control specialist wants to ensure the consistency of the filling process. From a simple random sample of $30$ bottles, the following statistics are obtained: $n=30$, $\bar{x}=498.7\text{ mL}$, $s=2.05\text{ mL}$.

Assume the population of fill volumes is normally distributed. At the $0.05$ significance level, test the claim that the standard deviation of the fill volume is less than $3.00\text{ mL}$.

A researcher claims that the population variance of exam scores is greater than $16$. A sample of $n=12$ students yields a sample variance of $s^2=24$. Test the claim at the $0.10$ significance level, assuming normality. What is the correct conclusion?

The monthly rent (in dollars) paid by $12$ randomly selected residents in a city is listed below:

$950$, $1020$, $990$, $980$, $1005$, $1015$, $995$, $1030$, $1010$, $1000$, $985$, $970$

At the $\alpha =0.05$ level of significance, is there sufficient evidence to conclude that the standard deviation of monthly rent is different from $\text{\$}25$? Assume the population is normally distributed.

A researcher claims that more than $40\%$ of adults prefer drinking coffee over tea. To test this claim, a random sample of $100$ adults is surveyed, and $47\%$ report preferring coffee. Using a significance level of $\alpha =0.01$, determine the critical value $z_{\text{crit}}$, and decide whether to reject or fail to reject the null hypothesis.

In a statistical test, the calculated test statistic is $t=2.4$. Does this value indicate that you should reject the null hypothesis?

A quality control analyst wants to determine whether the variability in the weight of small snack packets has decreased from what was previously known. She takes a random sample of $7$ packets and performs a left-tailed chi-square test at the $1\%$ significance level. What is the critical value and rejection region for this left-tailed chi-square test?

Which of the following statements is false regarding statistical hypotheses?

Why is a significance level of $\alpha =1$ not appropriate in hypothesis testing?

A gym advertises that the mean monthly membership fee is less than $\$55$. In testing this claim, which scenario describes a Type II error in testing this claim?