he amount of fight training times for student pilots at a training location has been roughly bell-shaped with mean 15 hours and standard deviation 2.5 hours. A few new instructors started training student pilots. The sample average of training times by the new instructors for 20 randomly selected students was 14 hours. The sample data didnít show any outliers or strong skewness. We want to determine if the average training time by the new instructors is less than 15 hours. Assuming that the standard deviation is still the same as the original population (that is 2.5 hours), do the following: (a) Consider the sampling distribution of sample means, x. Explain why its distibution is approximately normal, and then determine the standard deviation of x values. (b) If the mean of the population is 15 and standard deviation is 2.5, determine P( X < 14). (c) We want to conduct a suitable hypothesis at 5% level of signficance. Determine the relevant hypotheses for this test, and explain reasoning for your choice of the procedure (e.g. a z-test, t-test etc.). (d) Using your work above or using technology, determine the P-value of the test, and state your conclusion in the context given.
The amount of fight training times for student pilots at a training location has been roughly bell-shaped with
(a) Consider the sampling distribution of sample means, x. Explain why its distibution is approximately normal, and then determine the standard deviation of x values.
(b) If the mean of the population is 15 and standard deviation is 2.5, determine P( X < 14).
(c) We want to conduct a suitable hypothesis at 5% level of signficance. Determine the relevant hypotheses for this test, and explain reasoning for your choice of the procedure (e.g. a z-test, t-test etc.).
(d) Using your work above or using technology, determine the P-value of the test, and state your conclusion in the context given.
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