Question

A computer software vendor claims that a new version of their operating system will crash six times per year on average. Assume that the standard deviation is 3.6. A system administrator installs the operating system on a random sample of 41 computers. At the end of a year, the sample mean number of crashes is 5.1. Can you conclude that number of crashes per year is less than 6? a. Write in words what ? represents. b. State the null and alternative hypotheses. c. What is the sample evidence collected? ? = ?̅= d. Calculate the Z Test Statistic and label it on the graph. e. Is the sample mean significant? Explain. f. State your decision about the null hypothesis. g. Write your final conclusion about the alternative.

Answer 1

a. The  ? represents the new version of their operating system will crash six times per year on average

  b. The null and alternative hypotheses is ,

The test is left-tailed test

c. ? =41 , ?̅=5.1

d. The Z Test Statistic is ,

e. Yes.the sample mean significant

f. The critical value is , ; From Z-table

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject the null hypothesis.

g. Conclusion: There is not sufficient evidence to support the claim that the number of crashes per year is less than 6.