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- From: Mathematics, Statistics and Probability
- Posted on: Sat 23 Jan, 2016
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Whooping Crane Eggs
Once down to about 15, the world’s only wild flock of whooping cranes now numbers a record 237 birds in its Texas Coastal Bend wintering ground (www.SunHerald.com). The average whooping crane egg weighs 208 grams. A new batch of eggs was recently weighed, and their weights are listed below. At ? =0.01, is there sufficient evidence to conclude that the weight is greater than 208 grams?
210 208.5 211.6 212 210.3 210.2 209 206.4 209.7
Union Membership
Nationwide 13.7% of employed wage and salary workers are union members (down from 20.1% in 1983). A random sample of 300 local wage and salary workers showed that 50 belonged to a union. At ? = 0.05, is there sufficient evidence to conclude that the proportion of union membership differs from 13.7%?
Times of Videos
A film editor feels that the standard deviation for the number of minutes in a video is 3.4 minutes. A sample of 24 videos has a standard deviation of 4.2 minutes. At ? = 0.05, is the sample standard deviation different from what the editor hypothesized?
For this next exercise, perform these steps. Assume that all variables are normally or approximately normally distributed.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.
Driving for Pleasure - Two groups of drivers are surveyed to see how many miles per week they drive for pleasure trips. The data are shown. At ? = 0.01, can it be concluded that single drivers do more driving for pleasure trips on average than married drivers? Assume ?1 = 16.7 and ?2 = 16.1.
Single Drivers Married Drivers
106 110 115 121 132 97 104 138 102 115
119 97 118 122 135 133 120 119 136 96
110 117 116 138 142 139 108 117 145 114
115 114 103 98 99 140 136 113 113 150
108 117 152 147 117 101 114 116 113 135
154 86 115 116 104 115 109 147 106 88
107 133 138 142 140 113 119 99 108 105
Communication Times - According to the Bureau of Labor Statistics’ American Time Use Survey (ATUS), married persons spend an average of 8 minutes per day on phone calls, mail, and e-mail, while single persons spend an average of 14 minutes per day on these same tasks. Based on the following information, is there sufficient evidence to conclude that single persons spend, on average, a greater time each day communicating?
Use the 0.05 level of significance.
Single married
Sample size 26 20
Sample mean 16.7 minutes 12.5 minutes
Sample variance 8.41 10.24
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