A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 28 tires surveyed, the mean lifespan was 46,200 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? ote: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part ( a ) State the null hypothesis Ho: H 2 50,000 O Ho: H = 50,000 O Ho: H p-value, we do not reject the null hypothesis e a > p-value, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the avera res is less than 50,000. There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000. Part (i) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the and your lower and upper bounds to the nearest whole number.) 95% C.I. 46200 43384 x 49016 x Additional Materials eBookFrom generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. O Ho: M = 19 Ho: M = 19 O Ho: M = 19 O Ho: M = 19 Part (b) State the alternative hypothesis. O Hai H = 19 O Hai H = 19 Hail