Exam 12: Inference About a Population

Which of the following would be an appropriate null hypothesis?

To produce a confidence interval estimator for the total,we multiply the lower and upper confidence limits of the interval estimator of p by ____________________.

If we have some idea about the value of sample proportion ,we use that value in determining the sample size needed to estimate the population proportion p.

The sales manager of a large multinational corporation is concerned that some salespersons perform very well and others quite poorly.To help analyze the problem he draws a random sample of 20 salespersons,determines their commission incomes (in thousands of dollars),and calculates the following statistics: = $37.2,and s = $7.8.Do these statistics provide sufficient evidence at the 5% significance level to conclude that the population variance exceeds $35 million²?

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} Explain how to use the confidence interval to test the hypotheses at α = 0.10.

When a population is small,we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

If a sample has 18 observations and a 90% confidence estimate for μ is needed,the appropriate value of t is 1.740.

Because of the greater uncertainty,the t-statistic will display greater ____________________ than the z-statistic.

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} Estimate with 95% confidence thee number of Spanish adults who classify themselves as concerned about eating healthy.

The test statistic to test hypotheses about the population variance has a chi-squared distribution with n − 1 degrees of freedom when the population random variable has a(n)____________________ distribution.

A condition of using the chi-squared test statistic for testing the variance is that the population random variable have a normal distribution.

Socialist Party Voters A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that.In a test of hypothesis,H₀: p = 0.05 vs.H₁: p < 0.05,his random sample of size 1,000 registered voters revealed that the number of Socialists was 40. ​ ​ -{Socialist Voters Narrative} Construct a 95% confidence interval estimate of the population proportion and explain how to use it to test the hypotheses.

In determining the sample size needed to estimate the population proportion p,we let the sample proportion = 1 if we have no knowledge of even the approximate values of .

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} Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20.

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

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

Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. ​ ​ -{Physicians Narrative} Compute the p-value and explain how to use it to test the hypotheses.

____________________ refers to the mass production and marketing by a company of a single product for the entire market.

Which of the following would be an appropriate alternative hypothesis?

If the lower and upper confidence limits of the population proportion p,using a sample of size 1500,are 0.184 and 0.238,respectively,then the lower and upper confidence limits of the total number of successes in the population,given that the population size is 750,000,are respectively: