Seeking help with the following question
Seeking help with the following questions. Answers needed in 90 minutes, (by 3:30am EST). Thank
you!
1.) A researcher wishes to estimate, with 90% confidence, the population proportion of adults who are confident with their country’s banking system. His estimate must be accurate within 4% of the population proportion.
(a) No preliminary estimate is available. Find the minimum sample size needed.
(b) Find the minimum sample size needed, using a prior study that found that 26% of the respondents said they are confident with their country’s banking system.
(c) Compare the results from parts (a) and (b).
(a) What is the minimum sample size needed assuming that no prior information is available?
n = __
(Round up to the nearest whole number as needed.)
(b) What is the minimum sample size needed using a prior study that found that 26% of the respondents said they are confident with their country’s banking system?
n = __
(Round up to the nearest whole number as needed.)
(c) How do the results from (a) and (b) compare?
A.Having an estimate of the population proportion has no effect on the minimum sample size needed.
B.Having an estimate of the population proportion reduces the minimum sample size needed.
C.Having an estimate of the population proportion raises the minimum sample size needed.
2.) Assume the random variable x is normally distributed with mean μ=85 standard deviation σ=4. Find the indicated probability.
P(x<80)
P(x<80) = __
(Round to four decimal places as needed.)
3.) A population has a mean μ=80 and a standard deviation σ=22. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=253.
μx = __
(Simplify your answer.)
σx = __
(Type an integer or decimal rounded to three decimal places as needed.)
4.) In a survey of 637 males ages 18-64, 396 say they have gone to the dentist in the past year. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
The 90% confidence interval for the population proportion p is (__ , __)
(Round to three decimal places as needed.)
The 95% confidence interval for the population proportion p is (__, __)
(Round to three decimal places as needed.)
Interpret your results of both confidence intervals.
A.With the given confidence, it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.
B.With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.
C.With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.
Which interval is wider?
-The 90% confidence interval
-The 95% confidence interval
5.) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1 (see attachment for graph).
The area of the shaded region is __.
(Round to four decimal places as needed.
6.) In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.
(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is __.
(Round to four decimal places as needed.)
(b) Find the probability that a study participant has a height that is between 68 and 71
The probability that the study participant selected at random is between 68 and 71 inches tall is __.
(Round to four decimal places as needed.)
(c) Find the probability that a study participant has a height that is more than 71 inches.
The probability that the study participant selected at random is more than 71 inches tall is __.
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
A.There are no unusual events because all the probabilities are greater than 0.05.
B.The events in parts (a) and (c) are unusual because its probabilities are less than 0.05.
C.The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.
D.The event in part (a) is unusual because its probability is less than 0.05.
7.) Construct the confidence interval for the population mean μ.
c = 0.90, x overbar = 15.9, σ = 9.0, and n = 85
A 90% confidence interval for μ is (__,__) .
(Round to one decimal place as needed.)
8.) In a random sample of five microwave ovens, the mean repair cost was $60.00 and the standard deviation was $11.00. Assume the population is normally distributed and use a t-distribution to construct a 90% confidence interval for the population mean μ. What is the margin of error of μ? Interpret the results.
The 90% confidence interval for the population mean μ is (__, __).
(Round to two decimal places as needed.)
The margin of error is __.
(Round to two decimal places as needed.)
Interpret the results. Choose the correct answer below.
A.With 90% confidence, it can be said that the repair cost is between the bounds of the confidence interval.
B.It can be said that 90% of microwaves have a repair cost between the bounds of the confidence interval.
C.With 90% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval.
D.If a large sample of microwaves are taken approximately 90% of them will have repair costs between the bounds of the confidence interval.
9.) Find the probability and interpret the results. If convenient, use technology to find the probability.
The population mean annual salary for environmental compliance specialists is about $64,500. A random sample of 42 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $61,500? Assume σ = $6,200.
The probability that the mean salary of the sample is less than $61,500 is __.
(Round to four decimal places as needed.)
Interpret the results. Choose the correct answer below.
A.Only 0.09% of samples of 42 specialists will have a mean salary less than $61,500. This is an extremely unusual event.
B.About 0.09% of samples of 42 specialists will have a mean salary less than $61,500. This is not an unusual event.
C.Only 9% of samples of 42 specialists will have a mean salary less than $61,500. This is an extremely unusual event.
D.About 9% of samples of 42 specialists will have a mean salary less than $61,500. This is not an unusual event.
10.) Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed (see attached chart)l
The probability that the member selected at random is from the shaded area of the graph is __.
(Round to four decimal places as needed.)
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Question 10 Grpah.jpg
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