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From experience it is known that a certain brand of tyre lasts, on average, 15,000 miles...

From experience it is known that a certain brand of tyre lasts, on average, 15,000 miles with standard deviation 1,250. A new compound is tried and a sample of 120 tyres yields an average life of 15,150 miles, with the same standard deviation. Are the new tyres an improvement? Use p-value approach and assume 5% significance level

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Answer Date: 18/01/2019 To test the hypothesis is that the mean life of tire is improves 15000 miles at 5% significancelevel The null and alternative hypothesis is, H 0: μ-15000 Ha : μ > 15000 Thez-test statistics is, 15150 -15000 (1250/120) 1.31 The z-test statistics is 1.31The P-value for this test is, From the standard normal distribution table, the associated probability is 0.9049. Since find the area to the right,so subtract from 1 to get, Pz1.31) 1-(z <1.31) 1-0.9049 -0.0951 The P-value for this test is 0.0951 Decision The conclusion is that the p-value in this context is higher than 0.05 which is 0.0951, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that the mean life of tire is improves 15000 miles. The result is not statistically significant.

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