Question

Let μ1 denote true average tread life for a premium brand of P205/65R15 radial tire, and let μ2 denote the true average tread life for an economy brand of the same size. Test H0: μ1 − μ2 = 5000 versus Ha: μ1 − μ2 > 5000 at level 0.01, using the following data: m = 35, x = 42,100, s1 = 2500, n = 35, y = 36,900, and s2 = 1500. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = 0.4058 Correct: Your answer is correct. P-value = 0.5942 Incorrect: Your answer is incorrect.

Answer 1

we have

It is given that the mean difference for population is

Calculation for the test statistic

z =

setting the given values, we get

z =

on solving it, we get

z = 0.4058 (rounded to 4 decimals)

Now, we have to find the value of because it is a right tailed hypothesis

Using the identity

we can write it as

Using the z distribution table for right tailed hypothesis, we get = 0.6591 (check row-wise 0.4 and column-wise 0.01)

So, the required p value becomes

= 1 - 0.5691 = 0.3409 (rounded to four decimals)