Problems related to texts Chapter 7 73 to 74 1 Determine the

Problems related to text\'s Chapter 7 (7-3 to 7-4)
	1.	Determine the two chi-squared (?2) critical values for the following confidence levels and sample sizes.
		a.	95% and n=36
		b.	99% and n=18
	2.	We are also interested in estimating the population standard deviation (?) for all FHSU students\' IQ score. We will assume that IQ scores are at least approximately normally distributed. Below are the IQ scores of 30 randomly chosen students from FHSU campus.
		135	127	104	139	133	114	110	137	141	118
		115	118	121	141	112	134	115	132	132	118
		127	116	136	132	117	129	116	109	115	129
		Construct a 95% confidence interval estimate of sigma (?), the population standard deviation.
	3.	Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.
		a.	95% confidence	n=40	? known	population data believed to be normally distributed
			Appropriate distribution:
			Associated critical value:
		b.	90% confidence	n=31	? unknown	population data believed to be normally distributed
			Appropriate distribution:
			Associated critical value:
		c.	99% confidence	n=29	? unknown	population data believed to be skewed right
			Appropriate distribution:
			Associated critical value:
		d.	98% confidence	n=100	? known	population data believed to be very skewed
			Appropriate distribution:
			Associated critical value:

Solution

Problems related to text\'s Chapter 7 (7-3 to 7-4)

1.

Determine the two chi-squared (?²) critical values for the following confidence levels and sample sizes.

a.

95% and n=36

20.570, 53.203

b.

99% and n=18

5.697, 35.719

2

Construct a 95% confidence interval estimate of sigma (?), the population standard deviation.

n

24

mean

123.71

sample standard deviation

10.93

Data

Sample Size

24

Sample Standard Deviation

10.9285

Confidence Level

95%

Intermediate Calculations

Degrees of Freedom

23

Sum of Squares

2746.93858

Single Tail Area

0.025

Lower Chi-Square Value

11.6886

Upper Chi-Square Value

38.0756

Results

Interval Lower Limit for Variance

72.1443

Interval Upper Limit for Variance

235.0110

Interval Lower Limit for Standard Deviation

8.4938

Interval Upper Limit for Standard Deviation

15.3301

3.

Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.

a.

95% confidence

n=40

? known

population data believed to be normally distributed

Appropriate distribution: z

Associated critical value: 1.96

b.

90% confidence

n=31

? unknown

population data believed to be normally distributed

Appropriate distribution: z

Associated critical value: 1.645

c.

99% confidence

n=29

? unknown

population data believed to be skewed right

Appropriate distribution: t

Associated critical value: 2.763

d.

98% confidence

n=100

? known

population data believed to be very skewed

Appropriate distribution: z

Associated critical value: 2.326

Problems related to text\'s Chapter 7 (7-3 to 7-4)

1.

Determine the two chi-squared (?2) critical values for the following confidence levels and sample sizes.

a.

95% and n=36

20.570, 53.203

b.

99% and n=18 5.697, 35.719

2

Construct a 95% confidence interval estimate of sigma (?), the population standard deviation.

n 24 mean 123.71 sample standard deviation 10.93

Data Sample Size 24 Sample Standard Deviation 10.9285 Confidence Level 95% Intermediate Calculations Degrees of Freedom 23 Sum of Squares 2746.93858 Single Tail Area 0.025 Lower Chi-Square Value 11.6886 Upper Chi-Square Value 38.0756 Results Interval Lower Limit for Variance 72.1443 Interval Upper Limit for Variance 235.0110 Interval Lower Limit for Standard Deviation 8.4938 Interval Upper Limit for Standard Deviation 15.3301

3.

Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.

a.

95% confidence

n=40

? known

population data believed to be normally distributed

Appropriate distribution: z

Associated critical value: 1.96

b.

90% confidence

n=31

? unknown

population data believed to be normally distributed

Appropriate distribution: z

Associated critical value: 1.645

c.

99% confidence

n=29

? unknown

population data believed to be skewed right

Appropriate distribution: t

Associated critical value: 2.763

d.

98% confidence

n=100

? known

population data believed to be very skewed

Appropriate distribution: z

Associated critical value: 2.326