Problems related to text\'s Chapter 7 (7-3 to 7-4) 1. Determine the two chi-squa
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Question
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: 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:Explanation / Answer
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.
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.
n
24
mean
123.71
sample standard deviation
10.9285
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 (sample size >30)
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.
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.
n
24
mean
123.71
sample standard deviation
10.9285
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 (sample size >30)
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
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