3. a Briefly explain about the test statistic for testing population mean. 4 mar

Question

3. a Briefly explain about the test statistic for testing population mean. 4 marks) b) Briefly explain things need to be considered before you determine the critical value. (2 marks) The average running time of a certain variety of nickel-cadmium rechargeable flashlight battery is known to be 8.5 hours. A change in the production method for this battery has been proposed, and a sample of 60 batteries produced by the new method has mean running time of 8.62 hours and a standard deviation of 0.55 hour. i. If the new method product has no difference from the existing product c) in term of average running time, what conclusion do you reach at 0.05 level of significance? A chemical engineer examines the data and makes the inferences that the change in production was made for the purpose of improving the battery running time. He claims that the average running time of the new method is higher than the existing method. What conclusion does he reach at 0.05 level of significance? A second chemical engineer notes that the production method change might have been made for reasons such as reducing cost or increasing the number of times that the battery can be recharged. She claims that the major concern must be that the running time has not significantly worsened. What conclusion does she reach at 0.0 level of significance? (6 marks) ii. (4 marks) iii. 4 marks) **END OF QUESTIONS Page 4 of 9

Explanation / Answer

Q.3 (a) For testing population mean, we will use t test as sample mean has t distribution if population variance is unknown and would have z test as sample mean will have z distribution of population variance is known.

(b) We should take assumtion that the population is normally distributed. Sample is taken randomly.

(c) Here Test statistic for checking difference in methods

t = (xbar - H)/ (s/sqrt(n) = (8.62 - 8.50)/ (0.55/sqrt(60)) = 0.12 / 0.071 = 1.69

p- value = 2 * Pr(Z > 1.69) = 0.0482 * 2 = 0.0964

so at 0.05 level of significance, we shall say that statistically there is no difference from the existing methodn in term of average running time for battery.

(b)

Here Test statistic for checking if production metod wwas changed for the purpose of changing battery running time

t = (xbar - H)/ (s/sqrt(n) = (8.62 - 8.50)/ (0.55/sqrt(60)) = 0.12 / 0.071 = 1.69

so that will make it one - sided test

p- value = Pr(Z > 1.69) =1 - 0.9518 = 0.0482

so at 0.05 level of significance, we shall say that statistically there is significant difference from the existing method in term of average running time for battery.

(c)

Here Test statistic for checking if production metod wwas changed for the purpose of changing battery running time

t = (xbar - H)/ (s/sqrt(n) = (8.62 - 8.50)/ (0.55/sqrt(60)) = 0.12 / 0.071 = 1.69

so that will make it one - sided test because term like "worsened is used"

p- value = Pr(Z > 1.69) =1 - 0.9518 = 0.0482 > 0.01

so at 0.01 level of significance, we shall say that statistically there is no significant difference from the existing method in term of average running time for battery. So, her concern are not valid and running time has not worsened.

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