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A survey in the N.Y. Times Almanac finds the mean commute time (one way) is $25.4$ minutes for the $15$largest US cities. The Austin, TX chamber of commerce feels that Austin’s commute time is less and wants to publicize this fact. The mean for $25$randomly selected commuters is $22.1$minutes with a standard deviation of $5.3$minutes. At the $\mathrm{Î\pm }=$ $0.10$ level, is the Austin, TX commute significantly less than the mean commute time for the $15$largest US cities?

A report by the Gallup Poll found that a woman visits her doctor, on average, at most$5.8$times each year. A random sample of $20$women results in these yearly visit totals

$3;2;1;3;7;2;9;4;6;6;8;0;5;6;4;2;1;3;4;1$

At the α = 0.05 level can it be concluded that the sample mean is higher than $5.8$visits per year?

According to the N.Y. Times Almanac the mean family size in the U.S. is $3.18$. A sample of a college math class resulted in the following family sizes:

$5;4;5;4;4;3;6;4;3;3;5;5;6;3;3;2;7;4;5;2;2;2;3;2$

At $\mathrm{Î\pm }=0.05$ level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?

The student academic group on a college campus claims that freshman students study at least $2.5$ hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of $30$ freshman students and found a mean study time of $137$ minutes with a standard deviation of $45$ minutes. At $\mathrm{Î\pm }=0.01$ level, is the student academic group’s claim correct?

A sleeping bag is tested to withstand temperatures of$-15°\mathrm{F}$. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.

A sleeping bag is tested to withstand temperatures of $–15°F$. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.

In words, describe$1–\mathrm{β}$

In words, describe $1-\mathrm{β}$For Exercise $9.12$.

A sleeping bag is tested to withstand temperatures of$-15°\mathrm{F}$. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.

A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, ${\mathrm{H}}_0$, is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.

A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, $H_0$, is: the surgical procedure will go well. Which is the error with the greater consequence?

The power of a test is$0.981$.What is the probability of a Type II error?