Exam 11: Statistical Inference Concerning Variance

The following data,drawn from a normal population,are the waiting times (in minutes)of 12 randomly selected customers at a travel desk. 1.8 2.4 2.7 2.1 1.3 1.7 1.5 1.5 2.3 2.8 2.5 1.9 a.Calculate the point estimates of the population variance and the population standard deviation. b.Compute a 90% confidence intervals for the population variance and the population standard deviation.

Becky owns a diner and is concerned about sustaining the business.She wants to ascertain if the standard deviation of the profits for each week is greater than $250.The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916 Assume that profits are normally distributed.Which of the following is the correct value of the test statistic?

A financial analyst examines the performance of two mutual funds and claims that the variances of the annual returns for the bond funds differ.To support his claim,he collects data on the annual returns (in percent)for the years 2001 through 2010.The analyst assumes that the annual returns for the two emerging market bond funds are normally distributed.Use the following summary statistics. The competing hypotheses are At α = 0.10,is the analyst's claim supported by the data?

The value of the test statistic to test the ratio of two population variances is .

Construct a 95% confidence interval for the ratios of two population variances.The random samples of n₁ = 9 and n₂ = 11 with sample variances of = 500 and = 250,respectively.Assume that the samples were drawn from a normal population.

The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared.He would like to add an additional billing counter if the variance exceeds the cut-off.He checks the recent sample data.For a random sample of 24 customer waiting times,he arrives at a sample variance of 3.8 minutes-squared.The manager assumes the waiting times to be normally distributed.At α = 0.05,which of the following is the critical value ?

The value of the test statistic for the hypothesis test of the population variance,σ² is computed as = .

Amie Jackson,a manager at Sigma travel services,makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process.The travel website is open for reservations 24 hours a day,and Amie regularly checks the website for the waiting time to maintain consistency in service.She uses the following independently drawn samples of wait time during two peak hours,morning 8a.m.to 10 a.m.and evening 7p.m.to 9p.m. ,for the analysis.Assume that wait times are normally distributed. Which of the following is the correct hypotheses to determine if the variance of wait time during morning peak hours (population 1)differs from that during the evening peak hours (population 2)?

Becky owns a diner and is concerned about sustaining the business.She wants to ascertain if the standard deviation of the profits for each week is greater than $250.The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916 Assume that profits are normally distributed.Which of the following are an appropriate hypotheses to test Becky's concern?

A financial analyst examines the performance of two mutual funds and claims that the variances of the annual returns for the bond funds differ.To support his claim,he collects data on the annual returns (in percent)for the years 2001 through 2010.The analyst assumes that the annual returns for the two emerging market bond funds are normally distributed.Use the following summary statistics. For the competing hypotheses which of the following is the correct approximation of the p-value?

Consider the hypotheses H₀: σ² = 169,H_A:σ² ≠ 169.A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population.At 1% significance level,conduct a test for the population variance using the p-value approach.

Edmunds.com would like to test the hypothesis that the standard deviation for the age of an imported car on the road is greater than the standard deviation for the age of a domestic car.The following data shows the ages of a random sample of import and domestic cars. Which of the following would be the correct hypothesis test?

A financial analyst maintains that the risk,measured by the variance,of investing in emerging markets is more than 280(%)².Data on 20 stocks from emerging markets revealed the following sample results: = 12.1% and s² = 361(%)².Assume that the returns are normally distributed.Which of the following are appropriate hypotheses to test the analyst's claim?

The sampling distribution of is the χ² distribution.

For a sample of 10 observations drawn from a normally distributed population,we obtain the sample mean and the sample variance as 50 and 75,respectively.We want to determine whether the population variance is greater than 70.The critical value at a 5% significance level is

A random sample of 18 observations is taken from a normal population.The sample mean and sample standard deviation are 76.4 and 4.2,respectively.What is an 80% interval estimate of the population variance?

The sample standard deviation of the monthly sales (in thousands of dollars)of a telecommunications firm in the United States for two years,2010 and 2011,is computed as 6.7.Assuming that the sales data are drawn from a normally distributed population,conduct the following hypothesis tests for the population variance.Use the critical value approach at α = 0.05. a.H₀:σ₂ ≤ 25,H_A:σ² > 25 b.H₀:σ₂ = 36,H_A:σ² ≠ 36

The formula for the confidence interval of the population variance σ² is valid for the random samples drawn from any population.

A right-tailed test for the ratio of two population variances examines whether is greater than . .

Fizzco,a beverage manufacturing company,is interested in determining whether the standard deviation of their dispensing process has changed from a required level of 5 millimeters.They have taken a random sample of 12 bottles and have measured the amount of beverage dispensed into each bottle (in millimeters)as follows: 352 345 347 357 341 356 349 343 346 351 348 361 Which of the following is the correct 95% confidence interval of the population standard deviation?