Reference no: EM132316634
Statistics Assignment -
Instructions - Please answer each question.
Exercises 1 and 2 - Construct the indicated confidence interval for the population mean μ.
Exercise 1. c = 0.80, x- = 189, σ = 7.2, n = 76.
Exercise 2. c = 0.99, x- = 342, σ = 12.9, n = 53.
Exercise 3 - Coffee consumption: A researcher wants to estimate the mean annual coffee consumption in a geographic region. The coffee consumption in pounds for 25 randomly selected coffee drinkers from the region were gathered. Their coffee consumption is listed in the table below. Assume that σ = 3:9 and the coffee consumption follows a normal distribution. Find a 90% confidence for the population mean.
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7.9
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8.7
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6.1
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13.1
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9.2
|
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2.0
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10.5
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5.5
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3.0
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10.3
|
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9.0
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15.2
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3.5
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11.7
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15.5
|
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7.6
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4.8
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2.0
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9.8
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9.8
|
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11.5
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12.9
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6.2
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14.7
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8.6
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Exercises 4 and 5 - Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the samples are random and the population is normally distributed.
Exercise 4. c = 0.95, x- = 87, s = 6.2, n = 40.
Exercise 5. c = 0.98, x- = 562, s = 24.8, n = 27.
Exercise 6 - Soda consumption: An organization is interested in estimating the mean annual soda consumption of students at a college. The annual soda consumption in gallons of a random sample of 25 soda drinkers at the college is listed in the table below. Assume that the soda consumption follows a normal distribution. Find a 90% confidence interval for the population mean.
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16.2
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5.8
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22.2
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9.8
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12.7
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17.5
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4.7
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11.4
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16.2
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16.9
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7.1
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7.8
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21.4
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19.2
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11.8
|
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4.6
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12.5
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16.1
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19.9
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2.1
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17.6
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15.1
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19.1
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17.0
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9.5
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Exercise 7 - In a survey of 550 randomly selected women aged 25 or more in the U.S., 385 said they were paid less than men doing the same work. Construct a 90% confidence interval for the population proportion of women aged 25 or more in the U.S., who said they were paid less than men doing the same work.
Exercise 8 - In a survey of 325 randomly selected undergraduate students, 245 said that technology helped them to improve their grades. Construct a 80% confidence interval for the population proportion of students who feel that technology helped them to improve their grades.
Exercise 9 - In a survey of 400 randomly selected women, 115 said they preferred reading as a leisure time activity. Construct a 99% confidence interval for the population proportion of women who said they preferred reading as a leisure time activity.
Exercises 10 and 11 - Assume the samples are from populations that are normally distributed. Construct the indicated confidence intervals for both (a) the population variance σ2 and (b) the population standard deviation σ.
Exercise 10. c = 0.95, s2 = 17.5, n = 26.
Exercise 11. c = 0:99, s = 5.7, n = 42.
Exercise 12 - Resistors: A sample of 25 resistors were randomly selected from a manufacturing line. The population of these resistors is normal. The resistance measurements (ohms) for the resistors are listed in the table below. Construct a 99% confidence interval for the population standard deviation σ.
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1008
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994
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993
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1036
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1053
|
|
1056
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987
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987
|
970
|
1008
|
|
1030
|
1003
|
943
|
987
|
997
|
|
991
|
962
|
989
|
979
|
997
|
|
1010
|
1019
|
992
|
970
|
1029
|