Exam 12: Inference About a Population

A life insurance representative believes that the mean age of people who buy their first life insurance plan is less than 35.To test his belief he takes a random sample of 15 customers who have just purchased their first life insurance.Their ages are 42,43,28,34,30,36,25,29,32,33,27,30,22,37,and 40.There is not enough evidence to say the data are nonnormal.Can we conclude at the 1% significance level that the insurance representative is correct?

Mystic Pizza Mystic Pizza in Mystic,Connecticut,advertises that they deliver your pizza within 15 minutes of placing an order or it is free.A sample of 25 customers is selected at random.The average delivery time in the sample was 13 minutes with a sample standard deviation of 4 minutes. ​ ​ -{Mystic Pizza Narrative} What is the required condition of the technique used in the previous question?

A pharmaceutical company has just developed a new capsule to alleviate the symptoms of allergies and colds.However,they are concerned about the variability in the amount of time until the drug becomes effective.In a random sample of 10 individuals who suffer from allergies,the amount of time (in hours)for the capsule to take effect was recorded and listed as follows: 5,7,6,10,9,12,8,17,4,and 16.Estimate with 90% confidence the variance of the time for the drug to become effective.

The chi-squared distribution can be used in constructing confidence intervals and carrying out hypothesis tests regarding the value of a population variance.

In estimating the population mean μ when the population size N is small,the confidence interval estimator of μ is .

Science Quiz Scores Consider the hypotheses H₀: σ² = 20 vs.H₁: σ² > 20.Assume that Science scores on a 25-point quiz for a random sample of 5 students were drawn from a normal population.These were: 18,16,10,13,and 23. ​ ​ -{Science Quiz Scores Narrative} Estimate the population variance with 90% confidence.

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25.The upper limit of a 95% confidence interval for the population mean would equal:

In order to determine the p-value associated with hypothesis testing about the population mean μ,it is necessary to know the value of the test statistic.

When a population is small relative to the sample size,we must incorporate the ____________________ factor in the calculation of the standard error of estimate of the mean.

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 mean fee for car washers (including tips)is greater than 12?

Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. ​ ​ -{Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year,and explain how to use it to test the hypotheses.

Based on sample data,the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42.If the 10% level of significance were used in testing the hypotheses H₀: μ = 201 vs.H₁: μ ≠ 201,the null hypothesis:

____________________ populations allow us to use the confidence interval estimate of a mean to produce a confidence interval estimate of the population total.

Sinus Drug A company claims that 10% of the users of a certain sinus drug experience drowsiness.In clinical studies of this sinus drug,81 of the 900 subjects experienced drowsiness ​ ​ -{Sinus Drug Narrative} Explain how to use this confidence interval to test the hypotheses.

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold.Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22.Suppose the alternative we wanted to test was H₁: μ < 60.The correct rejection region for α = 0.05 is:

The t-distribution assumes that the population is normally distributed.

In a hypothesis test for the population variance,the hypotheses are H₀: σ² = 30 vs.H₁: σ² < 30.If the sample size is 20 and the test is being carried out at the 5% level of significance,the null hypothesis is rejected if:

Applicants' Grades The grades of a sample of 10 applicants,selected at random from a large population,are 71,86,75,63,92,70,81,59,80,and 90. ​ ​ -{Applicants' Grades Narrative} Compute the sample variance.

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} Is there sufficient evidence at the 5% significance level that the mousetrap will produce a profit?

Healthy Foods In segmenting the frozen meal market in Spain,a food manufacturer uses health and diet consciousness as the segmentation variable.Four segments are developed and coded as follows: 1: Concerned about eating healthy foods 2: Concerned about weight 3: Concerned about health because of illness 4: Unconcerned To distinguish between groups,surveys are conducted.On the basis of a questionnaire,people are categorized as belonging to one of these groups.A recent survey asked a random sample of 1,500 Spanish adults (20 and over)to complete the survey.Out of the 1,500 people surveyed,360 indicated that they are concerned about eating healthy foods.The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over. ​ ​ -{Healthy Foods Narrative} What is the objective of this problem?