Exam 12: Inference About a Population

Pilots' Union Contract A union composed of several thousand pilots is preparing to vote on a new contract.A random sample of 500 pilots yielded 320 who planned to vote yes.It is believed that the new contract will receive more than 60% yes votes. ​ ​ -{Pilots' Union Contract Narrative} Compute the p-value for the test.

Which of the following is an example illustrating the use of variance?

Assuming that all necessary conditions are met,what needs to be changed in the formula so that we can use it to construct a (1 − α)confidence interval estimate for the population proportion p?

To estimate the total number of successes in a large finite population of size N,using a sample of size n,the confidence interval estimator is:

Tractor Dealership An accountant was performing an audit for a tractor dealership.An auditor wants to examine the monetary error made by the purchasing order department in the month of July.He decided to randomly sample 100 of the 925 purchase orders for the month of July,and found the amount of error in each one.The statistics for this sample were: = $6.0 and s = $17.012. ​ ​ -{Tractor Dealership Narrative} Estimate with 95% confidence the total amount of monetary error for the month of July.

New Mousetrap After a financial analysis,the general manager of a large company decided that if more than 8% of potential buyers of a new mousetrap purchase that product,the company would show a profit.In a preliminary survey of 500 potential buyers,56 people say that they will buy the mousetrap. ​ ​ -{New Mousetrap Narrative} State the appropriate null and alternative hypotheses.

The sampling distribution of is approximately normal if the sample size is more than 30.

Tractor Dealership An accountant was performing an audit for a tractor dealership.An auditor wants to examine the monetary error made by the purchasing order department in the month of July.He decided to randomly sample 100 of the 925 purchase orders for the month of July,and found the amount of error in each one.The statistics for this sample were: = $6.0 and s = $17.012. ​ ​ -{Tractor Dealership Narrative} Why should the finite population correction factor (FPCF)be used for this problem? Explain.

Estimating or testing for p is used in situations when the data are ____________________.

If a sample has 15 observations and a 95% confidence estimate for μ is needed,the appropriate value of t is 1.753.

Mass marketing is especially effective for ____________________ goods such as gasoline,which are difficult to differentiate from the competition except through price and availability.

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90,a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin.The value of the test statistic in this problem is approximately equal to:

Concert Tickets A simple random sample of 100 concert tickets was drawn from a normal population.The mean and standard deviation of the sample were $120 and $25,respectively. ​ ​ -{Concert Tickets Narrative} Estimate the population mean with 90% confidence.

Single Mothers' Ages A random sample of 10 single mothers was drawn from a Obstetrics Clinic.Their ages are 22,17,27,20,23,19,24,18,19,and 24 years. ​ ​ -{Single Mothers' Ages Narrative} Estimate the population mean with 90% confidence.

A population is defined to be small if it is ____________________ than ____________________ times the size of the sample.

Generally speaking,mass marketing has given way to target marketing,which focuses on satisfying the demands of a particular segment of the entire market.

Concert Tickets A simple random sample of 100 concert tickets was drawn from a normal population.The mean and standard deviation of the sample were $120 and $25,respectively. ​ ​ -{Concert Tickets Narrative} Test the hypothesis H₀: μ = 125 vs.H₁: μ ≠ 125 at the 10% significance level.

Two uses for the population variance are to measure risk and consistency.

In forming a 95% confidence interval for a population mean from a sample size of 20,the number of degrees of freedom from the t-distribution equals 20.

Hourly Fees A random sample of 15 hourly fees for car washers (including tips)was drawn from a normal population.The sample mean and sample standard deviation were = $14.9 and s = $6.75. ​ ​ -{Hourly Fees Narrative} Can we infer at the 5% significance level that the population mean is greater than 12,assuming that you know the population standard deviation is equal to 6.75?