Statistics Problem Set: Developing Confidence Intervals

1. A car rental office checks out an average of 30 cars per day with a standard deviation of 8 cars. If a sample of 25 days of operation is selected and the sample mean is computed. What is the value for the standard error of the mean? What is the probability that the sample mean for the 25 days will be within 27 and 32 cars?

2. In an effort to estimate the mean annual amount spent per customer for groceries at a particular supermarket, data were collected for a sample of 100 households. The sample showed an average amount of $8,000. If the population standard deviation is $500. Develop an 80% then a 85% confidence interval estimate of the population mean annual amount spent. If the data were collected for a sample of 50 households rather than 100, develop an 85% confidence interval estimate of the population mean annual amount spent, assuming the population has a normal probability distribution

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1. A car rental office checks out an average of 30 cars per day with a standard deviation of 8 cars. If a sample of 25 days of operation is selected and the sample mean is computed,

(a) What is the value for the standard error of the mean?

Solution. Given that x-bar = 30, sigma = 8 and n = 25. Using a formula for the standard error of the mean: sigma_x-bar = sigma/(sqrt(n)) = 8/(sqrt(25)) = 1.6.

(b) What is the probability that the sample mean for the 25 days will be within 27 and 32 cars?
Solution. Let Z = (x-bar - 30)/1.6 . Then Z~N(0, 1). ...

Solution Summary

The expert develops confidence intervals and problem sets.

Are Confidenceintervals part of descriptive statistics or inferential statistics- why? Why would we use confidenceintervals instead of point estimates? Give an example of the use of a confidence interval and why you would prefer it over point estimates in your example.

In a statistics lecture, students are asked whether or not they enjoyed doing statistics. Random sample of 50 students was taken and 30 of them said that they enjoyed doing statistics. The lecturer claimed that more than 50% of the students enjoyed doing statistics.
(i) Test, at the 5% level of significance, whether or not

Confidenceintervals are used to help you get a better feel for your estimated value. Confidenceintervals are like nets. You don't know what the TRUE proportion value is so you throw a net (find a confidence interval based upon a survey). The confidence level indicates the percentage of times your net would "catch" the true pop

A criminology professor has been teaching graduate and undergraduate statistics for a few years. Her records show that the overall mean for final exam scores is 82 with a standard deviation of 10. The professor believes that this year's class is superior to her previous classes. She decides to conduct a test on the 25 students

See the data in the attached file and answer the following questions.
Question 1
Construct a 95% confidence interval for an average value of y given that x = 4. Remember the format is (x.xx, x.xx)
Question 2
Construct a 95% prediction interval for y given that x = 4.

We will be constructing confidenceintervals for the proportion of each color as well as the mean number of candies per bag.
Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies.
Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies.
Construct a 95% Confidence Interva

I need help completing this question:
A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.
Thank you for your assistance.

1. What do confidenceintervals represent? What is the most controllable method of increasing the precision (narrowing) of the confidence interval? What percentage of times will the mean (population proportion) not be found within the confidence interval?
2. As a sample size approaches infinity, how does the t distribution co