A sample of 250 observations is selected from a normal population for which the population standard deviation is known to be 25. The sample mean is 20. a. Determine the standard error of the mean. b. Explain why we can use formula to determine the 95 percent confidence interval. c. Determine the 95 percent confidence interval for the population mean

Suppose you know σ and you want an 85 percent confidence level. What value would you use to multiply the standard error of the mean by?

A research firm surveyed 49 randomly selected Americans to determine the mean amount spent on coffee during 1 week. The sample mean was $\$ 20$ per week. The population distribution is normal with a standard deviation of $\$ 5$. a. What is the point estimate of the population mean? Explain what it indicates. b. Using the $95 \%$ level of confidence, determine the confidence interval for $\mu$. Explain what it indicates.

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60. a. What is the point estimate of the population mean? b. Develop a 99 percent confidence interval for the population mean. c. Interpret the meaning of part (b).

A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a population standard deviation of $5. A sample of 49 steady smokers revealed that X̅ =$20. a. What is the point estimate of the population mean? Explain what it indicates. b. Using the 95 percent level of confidence, determine the confidence interval for μ. Explain what it indicates.

A normal population with a population standard deviation of 25 is used to sample a population of 250 observations. 20 is the sample mean. With this determine the 95% confidence interval for the population mean.

A sample of 49 observations is taken from a normal population with a standard deviation of 10 . The sample mean is 55 . Determine the $99 \%$ confidence interval for the population mean.

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of$250 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one bedroom apartments and finding the mean to be at least $1,950 per month?

Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a population standard deviation of 2.44 words per essay. For her 10 A.M. section of 40 students, the mean number of misspelled words was 6.05. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.

The owner of the West End Kwick Fill Gas Station wishes to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80 paid at the pump. a. Estimate the value of the population proportion. b. Develop a 95 percent confidence interval for the population proportion. c. Interpret your findings.

Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election. a. Estimate the value of the population proportion. b. Develop a 99 percent confidence interval for the population proportion.c. Interpret your findings.

Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of its testing program, Sony tests samples of 25 batteries. a. What can you say about the shape of the distribution of the sample mean? b. What is the standard error of the distribution of the sample mean? c. What proportion of the samples will have a mean useful life of more than 36 hours? d. What proportion of the sample will have a mean useful life greater than 34.5 hours? e. What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours?

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first nine times he filled up the tank, he found the mean was 23.4 miles per gallon with a sample standard deviation of 0.9 mpg. a.Compute the 95 percent confidence interval for his mpg.b. How many times should he fill his gas tank to obtain a margin of error below 0.1 mpg?

During a national debate on changes to health care, a cable news service performs an opinion poll of 500 small-business owners. It shows that 65 percent of small-business owners do not approve of the changes. Develop a 95 percent confidence interval for the proportion opposing health care changes. Comment on the result.