Mark each statement TRUE or FALSE. 1. 95\% of people wait between 4 and 6 minutes at the restaurant. 2. 95 of the people in your sample waited between 4 and 6 minutes. 3. You are 95\% sure your sample resulted in a confidence interval the contains the true mean.

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is ${\displaystyle \sigma =15}$
a) Compute the ${\displaystyle 95\mathrm{\%}}$ confidence interval for the population mean. Round your answers to one decimal place.
b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a ${\displaystyle 95\mathrm{\%}}$ confidence interval for the population mean. Round your answers to two decimal places.
c) What is the effect of a larger sample size on the interval estimate?
Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.

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?

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.

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. $(Z_{0.025}=1.96,Z_{0.005}=2.575)$

Assuming you are summing 10 poisson variables, and the sum of their results is 60, how would you approximate a ${\displaystyle 95\mathrm{\%}}$ CI for theta?

Can a 2 paired sample sets of size 15 (30 readings in total) be assumed to have normal distribution when finding confidence intervals?
I've seen that for large sample sizes (about 30 or more) the distribution tends to a normal distribution, but what if I have 2 sets of 15 which are paired? Would that count as a normal distribution, or would I need to use a t-distribution to approximate confidence intervals for the difference between their means?

A random sample of size ${\displaystyle n=25}$ from a normal distribution with mean ${\displaystyle \mu }$ and variance 36 has sample mean ${\displaystyle \bar{X}=16.3}$
a)
Calculate confidence intervals for ${\displaystyle \mu }$ at three levels of confidence: $80$. How to the widths of the confidence intervals change?
b) How would the CI width change if n is increased to 100?