Unformatted text preview: Course: Math 20] Fall B10
~- , p ‘ ..- Book: Larson: Elementary Statistics: Picturing the World, 5e
Date: 9/26/11 Time: 5:54 PM In a random sample of six microwave ovens, the mean repair cost was $80.00 and the standard deviation was
$12.50. Assume the variable is normally distributed and use a t—distribution to construct a 90% conﬁdence
interval for the population mean u. What is the margin of error of u? The ﬁrst step in constructing a conﬁdence interval for the population mean is to identify the sample statistics n,
x, and 5. Determine these values. 11: 6 X: 80. 5: 12.50 Next determine the critical value. For a t—distribution we need to ﬁrst ﬁnd the degrees of freedom, d.f. = n - 1.
Determine the degrees of freedom for this problem. d.f.= 5 The next step in determining the critical value is to‘ identify the conﬁdence level c. For this problem what is the
conﬁdence level? 0 = .90
Now use a t—distribution table or technology to determine the critical value tc.
tC = 2.015 In order to calculate the conﬁdence interval, next ﬁnd the margin of error E. The formula for the margin of error
E is shown below. 5
E = t — ° VI
Substitute the known values into the formula for the margin of error and evaluate. 12.50
E=2.015(—]= 10.28 , ~ V? A conﬁdence interval for the population mean is given by the following formula.
; ‘“ E < u < E + E
Substitute the known values into the formula for the conﬁdence interval and simplify. 80.00 — 10.28 < p < 80.00 + 10.28
69.72 < u< 90.28 Thus, the 90% conﬁdence interval for the population mean u is (69.72, 90.28) and its margin of error is 10.28.
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- Fall '11