Jc 46

Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:

(A)H0: µ = 63 and Ha: µ ≠63 a = 0.10

(B H0: µ ≤ 88 and Ha: µ >88 a = 0.01

(C)H0: µ ≥ 24 and Ha: µ <24 a = 0.05

I. Find the standard score (z) for a data value = 14.

II. Find the probability of a data value < 14.

III. Find the probability of a data value > 14.

Show all work. If someone can answer I will be thankful.

Determine the critical region and critical values for z that would be used to test the null hypothesis at the?

given level of significance, as described in each of the following: (A) Ho: μ=63 and Ha:μ ≠63, a=0.10 (B) Ho:μ ≤ 88 and Ha:μ> 88, a=0.01 (C)Ho > 24 and Ha: μ<24, a=0.05

Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work.

Class

Frequency

36-38

18

39-41

20

42-44

16

45-47

5

48-50

20

I just cannot figure out how to get the variance?

Class

Frequency

36-38

18

39-41

20

42-44

16

45-47

5

48-50

20 please show work.

The following data lists the average monthly snowfall for January in 15 cities around the US:

20 9 35 46 44 17 32 25

30 14 28 14 9 15 20

Find the mean, variance, and standard deviation. Please show all of your work.

A researcher claims that the average age of people who buy theatre tickets is 49. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 8. At a

= 0.05 is there enough evidence to reject the researcher’s claim? Show all work.

70

47

47

45

54

54

52

52

47

56

50

46

60

54

48

54

47

46

52

47

61

45

55

56

46

50

55

55

47

54

x y

1 5

2 8

3 11

4 14; How would the values of this table be interpreted in terms of linear regression?

Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work.

Class frequency

36-38 18

39-41 20

42-44 16

45-47 5

45-47 5

48-50 20

I understand how to get the mean and variance, I am having a hard time trying to understand the standard deviation?

- You want to show that people find the new design for a recliner chair more comfortable than the old design.

A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 145 was taken, and the mean amount spent was $191.89. Assuming a standard deviation equal to $42.49, find the 98% confidence interval for m, the mean for all such families (show all work).

. A 99% confidence interval estimate for a population mean was computed to be (31.1, 48.3). Determine the mean of the sample, which was used to determine the interval estimate (show all work).

Consider a normal population with µ = 25 and σ = 7.0.

(A) Calculate the standard score for a value x of 23.

(B) Calculate the standard score for a randomly selected sample of 45 with = 23.

(C) Explain why the standard scores of 23 are different between A and B above. (Points : 6)

By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.78 seconds.

Answer each of the following (show all work):

(A) How many measurements should be made in order to be 99% certain that the maximum error of estimation will not exceed 2.0 seconds?

(B) What sample size is required for a maximum error of 1.5 seconds?

and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is between 101.5 and 98.5.

Assume that a sample is drawn and z(α/2) = 1.65 and σ = 25. Answer the following questions:

(A)If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?

(B)Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?

(C)What happens to the Maximum Error of Estimate as the sample size gets larger?

(D)What effect does the answer to C above have to the size of the confidence interval?

A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 99% confident that her estimate is correct. If the standard deviation is 4.92, how large a sample is needed to get the desired information to be accurate within 0.71 decibels? Show all work.

The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.52 inches and a standard deviation of 0.46 inches. Show all work.

(A) What percentage of the grapefruits in this orchard is larger than 5.45 inches?

(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.45 inches?

Assume that the population of heights of female college students is approximately normally distributed with mean m of 68.66 inches and standard deviation s of 5.13 inches. A random sample of 67 heights is obtained. Show all work.

(A) Find the mean and standard error of the x̅ distribution

(B) Find P ( x̅ greater than 69.75)