Question

1)The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,528 hours. The population standard deviation is 1,080 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,228 hours. a. At the 0.05 level of​ significance, is there evidence that the mean life is different from 7,528 hours? b. Compute the​ p-value and interpret its meaning. c. Construct a 95​% confidence interval estimate of the population mean life of the light bulbs. d.Compare the results of​ (a) and​ (c). What conclusions do you​ reach?

2)The final scores of games of a certain sport were compared against the final point spreads established by odds makers. The difference between the game outcome and point spread​ (called a​ point-spread error) was calculated for 260 games. The mean error is x=−1.7. The population standard deviation of the​ point-spread error σ​= 12.2. Use this information to test the hypothesis that the true mean​ point-spread error for all games differs from 0.

Conduct the test at α=0.01 and interpret the result. Determine the null and alternative hypotheses. Choose the correct answer below.

A. H0​: μ0 ​≤ 0 Ha​: μ0> 0 B. H0​: μ0≠0 Ha​: μ0=0 C. H0​: μ0=0 Ha​: μ0≠0 D. H0​: μ0 ​≥ 0 Ha​: μ0< 0 The test statistic Z=enter your response here ​(Round to two decimal places as​ needed.) The ​p-value=enter your response here ​(Round to three decimal places as​ needed.)

3)A manufacturer produces plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 68 mm. To determine if this specification is​ met, random samples are taken from the production floor. One sample is contained in the table below. a. Determine if the process is not producing the tees to specification. Use a significance level of 0.05. b. If the hypothesis test determines the specification is not being​ met, the production process will be shut down while causes and remedies are determined. At times this occurs even though the process is functioning to specification. What type of statistical error would this​ be?

Answer 1

The questions pertain to hypothesis testing and confidence interval estimation using statistical methods such as the test of means, test statistic Z, and p-value, with a potential Type I error scenario in production quality control.

Step-by-step explanation:

The student's questions involve the application of statistical methods to hypothesis testing and confidence interval estimation. Regarding the first question, the test of means is used to determine if there is a significant difference between the sample mean and the known population mean of CFLs' life expectancy. The p-value and confidence interval are both tools to help make this determination. In the second question, the student is asked to perform hypothesis testing to ascertain the accuracy of odds makers' point-spreads using the test statistic Z and p-value. Lastly, the third scenario calls for hypothesis testing to see if plastic golf tees meet the manufacturer's length specification and mentions the possible occurrence of a Type I error if the process is incorrectly shut down.