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# Descriptive Statistics and Probability on a Sample

Question 1:

A quality control inspector randomly removed a small sample of light bulbs from an assembly line and turned them on, to see how long they would burn. Here are the numbers of hours her experiment produced: 972, 854, 952, 893, 945, 909, 850, 918, 909, 980, 926, 883, 925.
a. The first thing the inspector wants to know is whether she can be 95% certain that the average bulb from the factory burns at least 900 hours, as stated on its package.
i. What is the null hypothesis for her hypothesis test?
ii. What is the significance level of the test?
iii. What is the value of the test statistic she computes?
iv. What value of the test statistic is critical?
v. What numbers could she compare in order to make up her mind?
vi. How could she express her conclusion in language which any literate person could understand?
b. The second thing the inspector is worried about is if there is too much variation among the lifetimes of bulbs. She believes that the factory standard deviation should be no more than 35 hours.
i. What sort of statistical test should settle this question?
ii. Perform the test you selected, and explain to the inspector your basis for saying whether or not she has cause to be worried about the amount of variation.

Question 2:

Data set 25 in Appendix C of the textbook shows miscellaneous annual statistics.
a. Write the linear regression equation predicting the number of US murders and non-negligent homicides as a function of the annual number of sunspots.
b. Make the best prediction of the number of murders and non-negligent homicides if the number of annual sunspots will be 40.

#### Solution Summary

The solution provides step by step method for the calculation of descriptive statistics and probability . Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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