A sample of 51 research cotton samples resulted in a sample average percentage elongation of 8.19 and a sample standard deviation of 1.45. Calculate a 95% large-sample CI for the true average

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 the next 1000 98% Cis for mu that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of $\mu ?$
What isthe probability that between 970 and 990 of these intervals conta the corresponding value of ? (Hint: Let
Round your answer to four decimal places.)
‘the number among the 1000 intervals that contain What king of random variable s 2) (Use the normal approximation to the binomial distribution

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?

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?

Suppose you have selected a random sample of ? ${\displaystyle =14}$ measurements from a normal distribution. Compare the standard normal ? values with the corresponding ? values if you were forming the following confidence intervals.
a) $95\mathrm{\%}$ confidence interval
${\displaystyle ?=}$
${\displaystyle ?=}$
b) $80\mathrm{\%}$ confidence interval
${\displaystyle ?=}$
${\displaystyle ?=}$
c) $98\mathrm{\%}$ confidence interval
${\displaystyle ?=}$
${\displaystyle ?=}$

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: a) find the critical value ${\displaystyle t_{\frac{\alpha }{2}}}$. b) find the critical value ${\displaystyle z_{\frac{\alpha }{2}}}$, or c) state that neither the normal distribution nor the t distribution applies.
Here are summary statistics for randomly selected weights of newborn girls: ${\displaystyle n=249,\bar{x}=31.5hg,s=6.3hg}$. The confidence level is ${\displaystyle 95\mathrm{\%}}$.
A. ${\displaystyle t_{\frac{\alpha }{2}}=?}$
B. ${\displaystyle z_{\frac{\alpha }{2}}=?}$
C. Neither the normal distribution nor the t distribution applies.

A researcher is interested in finding a $90\mathrm{\%}$ confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 117 students who averaged 40.9 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.8 minutes. Round answers to 3 decimal places where possible.
a.
To compute the confidence interval use a ? distribution.
b.
With $90\mathrm{\%}$ confidence the population mean minutes of concentration is between ____ and ____ minutes.
c.
If many groups of 117 randomly selected students are studied, then a different confidence interval would be produced from each group. About ____ percent of these confidence intervals will contain the true population mean minutes of concentration and about ____ percent will not contain the true population mean number of minutes of concentration.