Question

A machine that paints traffic stripes on roads is mounted on a truck and set to a width of 4 inches. Road crews adjust the mount to ensure the width is correct. A road inspector checks the width of 40 random stripes to see if the machine has slipped out of adjustment. The mean diameter for this sample is x = 3.87 inches with a standard deviation of s = 0.5 inches. Does this indicate that the machine has slipped out of adjustment and the average width of stripes is no longer u = 4 inches? Use a 5% level of significance. Conduct a t test to examine whether the mean width of stripes is different from 4 inches. (a) Calculate the test statistic. (Round your answer to two decimal places.) (b) Calculate the p-value. (Use technology. Round your answer to four decimal places.)

Answer 1

Given, Sample size (n) - 40 Sample mean (7) = 3.87 Sample standard deviation(s) =0.5 Set up the null and the alterative hypothesis. H:u=4 Hu4 The test statistic for one sample t test is, S 3.87-4 0.5 140 =-1.64

b) P-value: P-value = [TDIST(1.64,39,2)] [Use Excel function] = 0.1090