Tutorial (Hypothesis testing) for hypothesis testing.pptx

Hypothesis testing

1. 21-Apr-20 1 Tutorial by Dr. Sumit Kumar Vishwakarma

2. Problem As part of the control program for a catalyst manufacturing line, the raw materials (alumina) are tested for purity. Authority suspects that whether or not true average purity of the alumina be 91. A random sample from a recent shipment of alumina yielded the following results (in %): 83.2 91.0 82.1 90.1 92.3 93.6 78.2 88.2 91.2 (Assume that the population distribution is normal) State the appropriate null and alternative hypothesis. Test the above hypothesis at 5% level of significance by clearly writing the critical region and test statistic. Sol: (a) (Two tailed test)  

3. (b) To test the above hypothesis We reject if or We will find, We have, the test statistic Thus, 1.821 < 2.306 Hence, we fail to reject  

4. Problem A manufacturer of sports equipment has developed a new synthetic fishing line that the company claims has a mean breaking strength of 8 kg with a standard deviation of 0.5 kg. Test the null hypothesis that against the alternative that if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kg. Use a 0.01 level of significance. Sol: (Two tailed test ) Given, Test statistic, Thus, , we reject  

5. Problem Let the test statistic Z have a standard normal distribution when is true. Give the significance level for each of the following situation: rejection region rejection region rejection region Sol: ( i ) (ii) (iii)  

6. Problem A single observation is to be used to test the null hypothesis that the mean waiting time between tremors recorded at a seismological station (the mean of an exponential distribution) is the alternative that hours. T he null hypothesis is to be rejected if the observed value if less than 8 or greater than 12, find the probability of a type I error. Sol: P( type-I error) = = 0.852  

7. Problem The melting point of each of 16 samples of a certain brand of hydrogenated vegetables oil was determined, resulting in Assume that the distribution of the melting point is normal with Test versus using a two-tailed level 0.01 test. If a level 0.01 test is used, what is the probability of a type II error when What value of n is necessary to ensure that when Sol: (a) Do not reject (b) 0.2266 (c) 22  

8. Questions from other (previous) topics Generate random variate X for the density function u sing the random numbers 34, 50, 75.  

9. End of Lecture