1.Suppose it is required that the mean opertaing life of batteries be 22 hours. Suppose also that the operating life of the batteries is normally distributed. Then suppose the standard deviation of the operating life of all such batteries is not known but that for the sample of 9 batteries the standard deviation is 3. If a sample of 9 batteries has a mean operating life of 20 hours, can we conclude that the mean operating life of batteries is not 22 hours?

• What hypothesis testing should be used?
• Compute for the test statistic?
• What is the critical value?
• In finding the critical value in the t-table, what degrees of freedom should be used?
• What should be the decision?

2.A consumer report shows that in testing 8 tires of goodyear the mean life of the tires was 20 000 km with a standard deviation of 2,500 km. Twelve tires of dunlop were tested under similar conditions with a mean life of 23,000 km and a standard deviation of 2,800 km. If a 0.05 level of significant is used, does the data present sufficient evidence to indicate a difference in the average life of the two brands of tires? Assume that the data are normally distributed. Assume equal population variances.

• What hypothesis testing should be used?
• Compute for the test statistic?
• What is the critical value?
• In finding the critical value in the t-table, what degrees of freedom should be used?
• What should be the decision?
• Which brand is better?