SOLUTION: A random sample of 23 people employed by the Florida state authority established they earned an average wage (including benefits) of $63 per hour. The sample standard deviation was
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-> SOLUTION: A random sample of 23 people employed by the Florida state authority established they earned an average wage (including benefits) of $63 per hour. The sample standard deviation was
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Question 922873: A random sample of 23 people employed by the Florida state authority established they earned an average wage (including benefits) of $63 per hour. The sample standard deviation was $6.1 per hour.
(a) What is your best estimate of the population mean? (Omit the "$" sign in your response.)
Estimated population mean $63
(b)
Develop a 99 percent confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.)
Confidence interval for the population mean wage is between ... and ....
(c)
How large a sample is needed to assess the population mean with an allowable error of $1 at 90 percent confidence? (Round up your answer to the next whole number.)
Sample size ....
I have already found the estimated population mean, but I am having trouble with the other two (b & c) questions. If you don't mind, please show your work so I can do these on my own in the future. Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website! sd(sample) = 6.1
(a) What is your best estimate of the population mean? (Omit the "$" sign in your response.) 63
Hi
Re TY...
1) asks for 2 decimal points
2) (small sample < 30)
b) 99% CI ((Round your answers to 2 decimal places)
SE = 6.1/sqrt(23)= 1.15
Sample is Small < 30, Using critical t-value(DF = 22) = 2.82
ME = 2.82SE = 2.82(1.15) = 3.24
Using two decimal points... IF not rounding off per mean:
CI: 63-3.24 < u < 63 + 3.24
CI: (59.76, 66.24)
.......
(c)
How large a sample is needed to assess the population mean with an allowable error of $1 at 90 percent confidence? (Round up your answer to the next whole number.)
ME = 1.645(6.1/sqrt(n)
1 = 1.645(6.1/sqrt(n))
n = [1.645(6.1)]^2 = 101 rounded Up
..........
= CI z = value
90% z =
92% z = 1.751
95% z = 1.96
98% z = 2.326
99% z = 2.576
..............
0.1 0.05 0.01 0.001
1 6.31 12.71 63.66 636.62
2 2.92 4.3 9.93 31.6
3 2.35 3.18 5.84 12.92
4 2.13 2.78 4.6 8.61
5 2.02 2.57 4.03 6.87
6 1.94 2.45 3.71 5.96
7 1.89 2.37 3.5 5.41
8 1.86 2.31 3.36 5.04
9 1.83 2.26 3.25 4.78
10 1.81 2.23 3.17 4.59
11 1.8 2.2 3.11 4.44
12 1.78 2.18 3.06 4.32
13 1.77 2.16 3.01 4.22
14 1.76 2.14 2.98 4.14
15 1.75 2.13 2.95 4.07
16 1.75 2.12 2.92 4.02
17 1.74 2.11 2.9 3.97
18 1.73 2.1 2.88 3.92
19 1.73 2.09 2.86 3.88
20 1.72 2.09 2.85 3.85
21 1.72 2.08 2.83 3.82
22 1.72 2.07 3.79
23 1.71 2.07 2.82 3.77
