Exam 9: Statistical Inferences Based on Two Samples

In a poll of 1,004 adults,934 indicated that restaurants and bars should refuse service to patrons who have had too much to drink.The 90% confidence interval for the proportion of all adults who feel the same way would be _____.

For a fixed sample size and standard deviation,the width of a confidence interval for a population mean $\mu$ will increase as the level of confidence decreases.

A psychologist is collecting data on the time it takes to learn a certain task.For 50 randomly selected adult subjects,the sample mean is 16.40 minutes and the sample standard deviation is 4.00 minutes.The 95% confidence interval for the mean time required by all adults to learn the task would be _____.

What sample size is needed to obtain a 90 percent confidence interval for the mean protein content of meat if the estimate is to be within 2 grams of the true mean value? Assume that the variance is 49 grams.

As the standard deviation decreases,the width of the confidence interval for a population mean _________.

The weight of a product is normally distributed.A sample of 50 units is taken from a batch.The sample yielded the following results: $\bar { x }$ = 75kg and s = 10kg. -Calculate a 99 percent confidence interval for $\mu$ .

As the significance level,? increases,the width of a confidence interval ________.

What is a 95 percent confidence interval for $\mu$ when n = 10, $\bar { x }$ = 34.1,and s = 3.0? Assume population normality.

When the level of confidence and sample proportion $\hat { p }$ remain the same,a confidence interval for a population proportion p based on a sample of n = 100 will be wider than a confidence interval for p based on a sample of n = 400.

A sample of 2,000 people yielded $\hat { p }$ =.52. -Calculate a 99 percent confidence interval for p.

A marketing research company surveyed grocery shoppers in the east and west coasts to see the percentage of the customers who prefer chicken to other meat.The data are given below. Sample size Number of customers in the sample that prefer chicken East Coast 492 156 West Coast 386 172 -Determine the 95% confidence interval for the difference between the proportion of customers who prefer chicken at the West Coast and the proportion of customers who prefer chicken at the East Coast.

A sample of 200 observations is taken.The mean is 31.7 and the standard deviation is 1.8.Assuming measurements follow a normal distribution,find a 90 percent confidence interval for the population mean.

The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late.The manager asked one of the planners to check the timeliness of shipments for 1000 orders.The planner randomly selected 1000 orders and found that 120 orders were shipped late.Construct the 95% confidence interval for the proportion of orders shipped late.

The success rate of a surgical procedure is 70 per 100 cases examined in a sample.Find a 90 percent confidence interval for the total number of successes per 1,000 cases.

Recently,a case of food poisoning was traced to a particular restaurant chain.The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur.Despite the response from the restaurant chain,many consumers refused to visit the restaurant for some time after the event.A survey was conducted three months after the food poisoning occurred with a sample of 319 patrons contacted.Of the 319 contacted,29 indicated that they would not go back to the restaurant because of the potential for food poisoning.The 95% confidence interval for the true proportion of the market who still refuse to visit any of the restaurants in the chain three months after the event would be _____.

A sociologist develops a test designed to measure a person's attitudes about disabled people,and 16 randomly selected subjects are given the test.Their mean score is 71.2 with a standard deviation of 10.5.If the score is normally distributed,the 99% confidence interval for the mean score of all subjects would be _____.

You wish to compute a confidence interval for a population proportion p.For a constant confidence level and sample size,which of the following values of $\hat { p }$ Will result in the interval with the shortest width?

Research has been conducted that studies the role that the age of workers has in determining the hours per month spent on personal tasks.A sample of 1,686 adults were observed for one month.The data are: AGE GROUP 18-24 25-44 45-64 Mean 4.17 4.04 4.31 Std Dev 0.75 0.81 0.82 241 768 677 A 98% confidence interval for the mean hours spent on personal tasks would be _____.

uppose that a realtor is interested in comparing the price of a starter home in two small cities.The realtor conducts a small survey in the two cities looking at the price of starter homes.Assume equal population variances and normally distributed populations. City A City B Sample Mean 86,900 84,000 Sample Std Dev 2300 1750 Sample Size 9 7 -Interpret the 95% confidence interval for the difference in mean price.

A market research company was interested in assessing how much money a single adult typically spent on groceries in one week.Participants were 772 single adults and the mean weekly grocery expenditure was found to be $69.70 with a standard deviation of $2.80.The 99% confidence interval for the mean weekly grocery expenditures for single adults would be _____.