Exam 12: Inference About a Population

The t-distribution is used in a confidence interval for a mean when the actual standard error is not known.

In testing a hypothesis about a population proportion p, the z test statistic measures how close the computed sample proportion has come to the hypothesized population parameter.

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

The statistic (n - 1)s² / $\sigma$ ² has a chi-squared distribution with n - 1 degrees of freedom if:

In estimating the population mean with the population standard deviation unknown, if the sample size is 16, there are 8 degrees of freedom.

The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and = 0.10, is 0.0247.

The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. -{Physicians Narrative} Can we conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24?

The width of a confidence interval estimate for a proportion will be:

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n -1 because we lose one degree of freedom by using the:

In a hypothesis test for the population variance, the hypotheses are H₀: $\sigma$ ² = 30 vs.H₁: $\sigma$ ² < 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:

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.

A robust estimator is one that is:

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.

Marketing segmentation separates consumers of a product into different groups in such a way that members of each group are ____________________ and there are differences between ____________________.

Which of the following would be an appropriate null hypothesis?

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: 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 parameter we wish to estimate? Explain.

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

Which of the following statements is correct regarding mass marketing?

Researchers determine 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.Using the sample information provided, the value of the test statistic is: