In: Statistics and Probability

Construct a 90% confidence interval to estimate the population mean using the accompanying data. What assumptions need to be made to construct this interval?

x=59 σ=15 n=17

What assumptions need to be made to construct this interval?

A. The population is skewed to one side.

B. The sample size is less than 30.

C. The population must be normally distributed.

D. The population mean will be in the confidence interval.

With 90% confidence, when n=17, the population mean is between the lower limit of and the upper limit of .

Solution :

Given that,

Point estimate = sample mean =
= 59

Population standard deviation =
= 15

Sample size = n = 17

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2
=0.10/ 2= 0.05

Z/2
= Z_{0.05 = 1.645}

Z/2
= 1.645

Margin of error = E = Z/2
* (
/n)

= 1.645 * ( 15/ 17 )

= 5.98

At 90 % confidence interval estimate of the population mean is,

- E <
<
+ E

59 - 5.98 <
< 59+ 5.98

53.02 <
< 64.98

( 53.02,64.98 )

**Answer** D. The population mean will be in the
confidence interval.

With 90% confidence, when n=17, the population mean is between the lower limit of =53.02 and the upper limit of =64.98.

Construct a 95?% confidence interval to estimate the population
mean using the following data. What assumptions need to be made to
construct this? interval?
x?=93
?=15
n=17
With 95?% ?confidence, when n=17 the population mean is between
the lower limit of __ and the upper limit of __

Construct a 99% confidence interval to estimate the population
mean using the data below. What assumptions need to be made about
this population?
x overbar =32
s=9.1
n=28

Construct a 95% confidence interval to estimate the population
mean using the following data. What assumptions need to be made to
construct this interval?
x(over bar x)= 83 s=19 n=16
What assumptions need to be made to construct this
interval?
A. The population is skewed to one side.
B. The sample size is less than 30.
C. The population mean will be in the confidence interval.
D. The population must be normally distributed.
With 95% confidence, when n=16 the population...

Refer to the accompanying data set and construct a 90%
confidence interval estimate of the mean pulse rate of adult
females; then do the same for adult males. Compare the results.
LOADING... Click the icon to view the pulse rates for adult females
and adult males. Construct a 90% confidence interval of the mean
pulse rate for adult females. nothing bpmless thanmuless than
nothing bpm (Round to one decimal place as needed.) Construct a
90% confidence interval of the mean...

Refer to the accompanying data set and construct a 90%
confidence interval estimate of the mean pulse rate of adult
females; then do the same for adult males. Compare the results.
Males Females
87 77
74 92
51 56
60 65
54 54
61 83
51 78
77 85
49 89
62 55
74 34
59 68
66 81
76 79
80 79
63 66
64 66
96 80
45 58
85 61
72 82
62 85
73 72
71 ...

Refer to the accompanying data set and construct a 90%
confidence interval estimate of the mean pulse rate of adult
females; then do the same for adult males. Compare the results.
Males Females
82 83
72 94
48 59
57 64
54 56
62 80
53 78
74 86
53 86
63 58
73 35
61 65
65 85
76 76
83 75
65 64
64 68
93 79
41 59
84 63
74 82
64 82
72 68
70 ...

Refer to the accompanying data set and construct a 90%
confidence interval estimate of the mean pulse rate of adult
females; then do the same for adult males. Compare the results.
Pulse Rates (beats per minute)
Males Females
82 83
72 94
48 59
57 64
54 56
62 80
53 78
74 86
53 86
63 58
73 35
61 65
65 85
76 76
83 75
65 64
64 68
93 79
41 59
84 63
74 82...

Refer to the accompanying data set and construct a 90%
confidence interval estimate of the mean pulse rate of adult
females; then do the same for adult males. Compare the results.
Males
Females
85
71
79
82
71
66
94
79
52
75
59
70
58
74
65
77
53
56
54
86
62
66
83
88
52
58
76
89
79
79
86
91
53
70
88
9
61
65
57
96
72
61
38
69
57
98
64...

Refer to the accompanying data set and construct a 90%
confidence interval estimate of the mean pulse rate of adult
females; then do the same for adult males. Compare the results.
Males
Females
83
79
74
96
51
56
61
67
53
55
59
83
53
78
78
84
52
90
63
58
69
37
61
64
67
86
76
76
80
78
65
64
68
66
97
76
45
62
86
66
75
83
61
80
70
72
73...

Construct a 95% confidence interval to estimate the population mean using the data below. What assumptions need to be made about this population? x̄ = 33 s= 9.9 n=27 The 95% confidence interval for the population mean is from a lower limit of _______ to an upper limit of _______ .

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