The local energy company claims the average annual electricity bill for its subscribers is just $600. A consumer watchdog group wants to dispute this

In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 358 ​trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d).
a) Given that Emily used a coin toss to select either her right hand or her left​ hand, what proportion of correct responses would be expected if the touch therapists made random​ guesses? ​(Type an integer or a decimal. Do not​ round.)
b) Using​ Emily's sample​ results, what is the best point estimate of the​ therapists' success​ rate? ​(Round to three decimal places as​ needed.)
c) Using​ Emily's sample​ results, construct a ${\displaystyle 90\mathrm{\%}}$ confidence interval estimate of the proportion of correct responses made by touch therapists.
Round to three decimal places as​ needed - ?${\displaystyle <p<}$?

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 298 accurate orders and 51 that were not accurate. a. Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: ${\displaystyle 0.127<p<0.191}$. What do you​ conclude? a. Construct a 90​% confidence interval. Express the percentages in decimal form. ___

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?

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

In a survey of 2085 adults in a certain country conducted during a period of economic?
Uncertainty, ${\displaystyle 63\mathrm{\%}}$ thought that wages paid to workers in industry were too low. The margin of error was 8 percentage points with ${\displaystyle 90\mathrm{\%}}$ confidence.
For parts (1) through (4) below, which represent a reasonable interpretation of the survey results. For those that are not reasonable, explain the flaw.
1) We are ${\displaystyle 90\mathrm{\%}}$ confident ${\displaystyle 63\mathrm{\%}}$ of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
2) We are ${\displaystyle 82\mathrm{\%}}$ to ${\displaystyle 98\mathrm{\%}}$ confident ${\displaystyle 63\mathrm{\%}}$ of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. Is the interpretation​ reasonable?
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
3) We are ${\displaystyle 90\mathrm{\%}}$ confident that the interval from 0.55 to 0.71 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low.
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
4) In ${\displaystyle 90\mathrm{\%}}$ of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.55 and 0.71.
A) The interpretation is reasonable.
B) The interpretation is flawed. The interpretation provides no interval about the population proportion.
C) The interpretation is flawed. The interpretation sugguests that this interbal sets the standard for all the other intervals, which is not true.
D) The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

Of 1000 randomly selected cases of lung cancer 843 resulted in death within 10 years. Construct a ${\displaystyle 95\mathrm{\%}}$ two-sided confidence interval on the death rate from lung cancer.
a) Construct a ${\displaystyle 95\mathrm{\%}}$ two-sides confidence interval on the death rate from lung cancer. Round your answer 3 decimal places.
${\displaystyle ?\le p\le ?}$
b) Using the point estimate of p obtained from the preliminary sample what sample size is needed to be ${\displaystyle 95\mathrm{\%}}$ confident that the error in estimatimating the true value of p is less than 0.00?
c) How large must the sample if we wish to be at least ${\displaystyle 95\mathrm{\%}}$ confident that the error in estimating p is less than 0.03 regardless of the value of p?

Construct a 95% confidence interval for the true average monthly salary earned by all employees of People Plus Pty, if it was found that the average monthly salary earned by a sample of 19 employees of the company was R18 500, with a standard deviation of R1 750. Interpret your answer