To understand its customer base, a mail-order book club needs to know something

QUESTION

1. To understand its customer base, a mail-order book club needs to know something about the frequency with which customers make subsequent purchases. They collect data on the number of purchases that customers make during their initial three year membership. From a set of randomly selected customers they obtain the following data. 28 26 25 25 23 25 22 20 24 26 27 27 27 23 21 24 28 25 21 24 27Is there evidence that the average number of purchase (m) is at least 24. That is test H0: µ <= (less than or equal to) 24 Vs H1:µ> 24.Use 5% level of significance and p-value approach. Show all six steps.2. For the following tests and the t values, find the p-values. . Also use 5% level of significance to draw a conclusion as to whether you reject or not reject the null hypothesis.Right tailed test with .67 with Left tailed test with t= -2.50 n= 19 (iii) Two tailed test with t= 2.14 with a sample size n= 193. The CEO of a company believes that at least 70% of the employees are over 30 years old. A random sample of 200 employees revealed that 150 of them are over 30 years old. Is there evidence to justify the statement of the CEO at 5% level of significance. (test H0: P<= (less than or equal to) 0.70 vs H1 : P > 0.70). Use p-value approach. Show all six steps.4. A manufacturer of gunpowder has developed a new powder that is designed to produce a muzzle velocity equal to 3000 feet per second. Eight shells are loaded with the charge and muzzle velocities are measured. The resulting velocities are : 3005 2925 2935 2965 2995 3005 2935 2905. Do the data present sufficient evidence to indicate the average velocity differs from 3000 feet per second? That is, test H0: µ against H1: µ ?3000. Use ?=.10 Use p-value approach

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