True or False? A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participan

A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers.
Assume the distribution of measurements to be approximately normal.
a) Construct a ${\displaystyle 99\mathrm{\%}}$ confidence interval for the average number of kilometers an automobile is driven annually in Virginia.
b) What can we assert with ${\displaystyle 99\mathrm{\%}}$ confidence about the possible size of our error if we estimate the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
Construct the ${\displaystyle 95\mathrm{\%}}$ confidence interval estimate of the mean wake time for a population with the treatment.
$min<\mu <min$ ​(Round to one decimal place as​ needed.)
What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let j: denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence intervals (7-8, 9.6)
(a) Would 2 90%% confidence interval calculated from this same sample have been narrower or wider than the glven interval? Explain your reasoning.
(b) Consider the following statement: There is 9 95% chance that Is between 7.8 and 9.6. Is this statement correct? Why or why not?
(c) Consider the following statement: We can be highly confident that 95% of al bottles ofthis type of cough syrup have an alcohol content that is between 7.8 and 9.6. Is this statement correct? Why or why not?

The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be 2.6 grams per liter. Find the 95% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3 gram per liter. $(Z_{0.025}=1.96,Z_{0.005}=2.575)$

Consider two independent distributions that are mound-shaped. A random sample of size $n_1=36$ from the first distribution showed $x_1=15$, and a random sample of size $n_2=40$ from the second distribution showed $x_2=14$. Based on the confidence intervals you computed, can you be 95% confident that ${\mu }_1$ is larger than ${\mu }_2$? Explain.

The number of rescue calls received by a rescue squad in a city follows a Poisson distribution with 2.83 per day. The squad can handle at most four calls a day.
a. What is the probability that the squad will be able to handle all the calls on a particular day?
b. The squad wants to have at least ${\displaystyle 95\mathrm{\%}}$ confidence of being able to handle all the calls received in a day. At least how many calls a day should the squad be prepared for?
c. Assuming that the squad can handle at most four calls a day, what is the largest value of that would yield ${\displaystyle 95\mathrm{\%}}$ confidence that the squad can handle all calls?

A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city. Construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna​ sushi?
$\begin{array}{|ccccccc|}\hline 0.60& 0.82& 0.09& 0.89& 1.29& 0.49& 0.82\\ \hline\end{array}$
What is the confidence interval estimate of the population mean ${\displaystyle \mu ?}$
${\displaystyle ?p\pm <\mu <?p\pm }$