4000 B.C. skull breadths5.1604128.69128.692.131V16toV16150 A.D. skull breadths136.25136.25V16toV16of(c) Using the formulas from part (b), find the 95% confidence intervals for the mean maximum skullbreadths of all Egyptian skulls from each period. Round each answer to the nearest hundredth (2 decimalplaces).4000 B.C. skull breadths125.938X mm to 131.437X mm150 A.D. skull breadthsmm tomm(d) Based on these confidence intervals, can we conclude with 95% certainty that the true population mean Archeologists have discovered a sample of ancient Egyptian skulls from two different time periods, 4000B.C. and 150 A.D. They believe that the mean maximum skull breadth (the width of the skull at its widestpart) has increased from 4000 B.C. to 150 A.D. A sample of 16 Egyptian skull breadths (in mm) from eachtime period is show below:4000 BC133 137130131130131123130121124 136124130 123122 134150 AD139141 141136 137 131139 128133 141 134140131 141128140(a) Calculate the mean and standard deviation for each data set. Round each mean to 2 decimal places,and each standard deviation to 4 decimal places.4000 BC mean: 128.6876x o150 AD mean: 136.25004000 BC standard deviation: 5.1603150 AD standard deviation: 4.7679(b) Using your answers from part (a) and the formula for a 95% confidence interval as presented inlecture, fill in the blanks with the appropriate values for this problem for calculating the confidenceinterval below.• To enter Va where x is any number, type sqrt(x). For example, 2 should be written as sqrt(2).• Round the t-score to 2 decimal places.O30

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Description: 4000 B.C. skull breadths5.1604128.69128.692.131V16toV16150 A.D. skull breadths136.25136.25V16toV16of(c) Using the formulas from part (b), find the 95% confidence intervals for the mean maximum skullbreadths of all Egyptian skulls from each period. R

The mean value is approximated to 2 decimal places and the standard deviation value is approximated…

Math

Statistics

133 137 130 131 130 131 123 130 121 124 136 124 130 123 122 134 150 AD 140 136 137 131 139 139 141 141 128 131 141 133 141 134 128 140 (a) Calculate the mean and standard deviation for each data set. Round each mean to 2 decimal places, and each standard deviation to 4 decimal places. 4000 BC mean: 128.6876 150 AD mean: 136.2500 4000 BC standard deviation: 5.1603 150 AD standard deviation: 4.7679 (b) Using your answers from part (a) and the formula for a 95% confidence interval as presented in lecture, fill in the blanks with the appropriate values for this problem for calculating the confidence interval below. • To enter Va where x is any number, type sqrt(x). For example, v2 should be written as sqrt(2). • Round the t-score to 2 decimal places.

133 137 130 131 130 131 123 130 121 124 136 124 130 123 122 134 150 AD 140 136 137 131 139 139 141 141 128 131 141 133 141 134 128 140 (a) Calculate the mean and standard deviation for each data set. Round each mean to 2 decimal places, and each standard deviation to 4 decimal places. 4000 BC mean: 128.6876 150 AD mean: 136.2500 4000 BC standard deviation: 5.1603 150 AD standard deviation: 4.7679 (b) Using your answers from part (a) and the formula for a 95% confidence interval as presented in lecture, fill in the blanks with the appropriate values for this problem for calculating the confidence interval below. • To enter Va where x is any number, type sqrt(x). For example, v2 should be written as sqrt(2). • Round the t-score to 2 decimal places.

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

Topic Video

Question

100%

4000 B.C. skull breadths
5.1604
128.69
128.69
2.131
V16
to
V16
150 A.D. skull breadths
136.25
136.25
V16
to
V16
of
(c) Using the formulas from part (b), find the 95% confidence intervals for the mean maximum skull
breadths of all Egyptian skulls from each period. Round each answer to the nearest hundredth (2 decimal
places).
4000 B.C. skull breadths
125.938
X mm to 131.437
X mm
150 A.D. skull breadths
mm to
mm
(d) Based on these confidence intervals, can we conclude with 95% certainty that the true population mean

Archeologists have discovered a sample of ancient Egyptian skulls from two different time periods, 4000
B.C. and 150 A.D. They believe that the mean maximum skull breadth (the width of the skull at its widest
part) has increased from 4000 B.C. to 150 A.D. A sample of 16 Egyptian skull breadths (in mm) from each
time period is show below:
4000 BC
133 137
130
131
130
131
123
130
121
124 136
124
130 123
122 134
150 AD
139
141 141
136 137 131
139 128
133 141 134
140
131 141
128
140
(a) Calculate the mean and standard deviation for each data set. Round each mean to 2 decimal places,
and each standard deviation to 4 decimal places.
4000 BC mean: 128.6876
x o
150 AD mean: 136.2500
4000 BC standard deviation: 5.1603
150 AD standard deviation: 4.7679
(b) Using your answers from part (a) and the formula for a 95% confidence interval as presented in
lecture, fill in the blanks with the appropriate values for this problem for calculating the confidence
interval below.
• To enter Va where x is any number, type sqrt(x). For example, 2 should be written as sqrt(2).
• Round the t-score to 2 decimal places.
O30

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