The following data represent the total weekly studying time in hours for a group

Question

The following data represent the total weekly studying time in hours for a group of 20 students: 18, 18, 29, 17, 28, 25, 11, 14, 15, 20, 14, 23, 13, 17, 23, 18, 30, 14, 17, 18 use the given data to answer the following questions.

a. Construct a 96% confidence interval of mean weekly studying time of all students.

b. Construct a 95% confidence interval of standard deviation of weekly studying time of all students.

c. Test the claim that the mean weekly studying time of all students is less than 20 hours.

d. Test the claim that the standard deviation of weekly studying time of all students is 5 hours.

e. If the researchers want the error of estimating the mean studying time is no more than 2.5 hours, find the sample size needed if the C-level is 98%

Explanation / Answer

Lower limit = M - (tCL)(sM)
Upper limit = M + (tCL)(sM)

tcl = 2.093

a)

b)

Z = 1.96

c)

Since the T critical value is 2.093 and the calculated t value is 0.56, Hence we accept null Hypothesis and conclude that the mean weekly studying time of all students is not less than 20 hours

b)

SD of given data = 5.57

Hypothesied SD = 5

F= 5.57 / 5 = 1.12

F crictical value = 3.10

Since the calculared value is 1.12 less than 3.10, hence we accept the null hypothesis and conclude that the standard deviation of weekly studying time of all students is not 5 hours

X 18 18 29 17 28 25 11 14 23 13 17 23 13 17 23 18 30 14 17 18 Total 386 Mean(M) 19.3 Variance 31.06 Standard Error(Sm) 1.25

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