You should submit a hard copy to me if possible. You’ll need to use MINITAB for
ID: 3358366 • Letter: Y
Question
You should submit a hard copy to me if possible. You’ll need to use MINITAB for questions 3 and 4 but not for questions 1 and 2.
1.A research study shows that the yearly cost of dental claims for Virginia state employees with dental care as a part of their health insurance has a distribution with a mean of $1200 and a standard deviation of $200. If a random sample of 25 Virginia state employees with dental insurance is selected, what is the probability that the mean of the yearly dental claims for this sample is between $1175 and $1225?
2. How reliable are the results of political polls? Suppose, hypothetically, that one of the gubernatorial candidates, RN, is favored by exactly 50% of all registered voters in Virginia. Suppose further that a random sample of 1000 registered Virginia voters is selected. What is the probability that, in this sample, the percentage that favor RN is less than 47%? (HINT: Remember that 50% and 47% are equivalent to .50 and .47 when expressed as proportions in the relevant formulas.)
3. Consider the data in problem 2.38 on page 63. This data consists of the cost of electricity during July 2013 for a random sample of 50 one-bedroom apartments in the New York City area. It is included in the data file, UTILITY.
a) Using this data, construct a 90% confidence interval for the population mean cost of electricity for all such apartments in July 2013.
b) Briefly explain the meaning of this interval.
c) What is the margin of error when estimating the population mean cost of electricity during 2013 for one-bedroom apartments in that area? (HINT: You can determine the margin of error from the confidence interval determined in part a))
d) Statistical theory (the Central Limit Theorem) indicates that the interval created in part a) may not be as reliable if the population shape is highly skewed. However, with a sample size of 50, only extreme skewness would be a concern. Using the data in the sample of 50 electricity bills, determine if you think this shape is highly skewed. (HINT: Methods for doing so were discussed in chapters 2 and 3. Ultimately, this is a subjective decision and so you just need to state your opinion and attempt to justify it with appropriate statistical evidence).
4. Consider the data in problem 2.37 on page 63. This data consists of the caffeine content (in milligrams per ounce) for a random sample of 26 energy drinks. It is included in the data file, CAFFEINE, and is also listed below.
3.2 1.5 4.6 8.9 7.1 9.0 9.4 31.2 10.0 10.1 9.9 11.5
11.8. 11.7 13.8 14.0 16.1 74.5 10.8 26.3 17.7 113.3 32.5
14.0 91.6 127.4
a) Construct a 95% confidence interval for the mean caffeine content for the population of energy drinks.
b) Statistical theory (the Central Limit Theorem) indicates that the interval created in part a) may not be reliable if the population shape is highly skewed. Using the data in the sample of 26 drinks, determine if you think this shape is highly skewed. (HINT: Methods for doing so were discussed in chapters 2 and 3. Ultimately, this is a subjective decision and so you just need to state your opinion and attempt to justify it with appropriate statistical evidence).
MINI TAB
Caffeine per fluid ounce (mg/oz
3.2
1.5
4.6
8.9
7.1
9.0
9.4
31.2
10.0
10.1
9.9
11.5
11.8
11.7
13.8
14.0
16.1
74.5
10.8
26.3
17.7
113.3
32.5
14.0
91.6
127.4
Utility Charge
96
171
202
178
147
102
153
197
127
82
157
185
90
116
172
111
148
213
130
165
141
149
206
175
123
128
144
168
109
167
95
163
150
154
130
143
187
166
139
149
108
119
183
151
114
135
191
137
129
158
Explanation / Answer
(1) = 1200, = 200, n = 25
z1 = (x1 - )/(/n) = (1175 - 1200)/(200/25) = -0.625 and z2 = (x2 - )/(/n) = (1225 - 1200)/(200/25) = 0.625
P(1175 < x-bar < 1225) = P(-0.625 < z < 0.625) = 0.468
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