Question

In: Statistics and Probability

Refer to the accompanying data set and construct a 90​% confidence interval estimate 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

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

90

67

55

85

85

80

63

75

79

80

56

81

75

64

56

64

55

68

65

64

102

97

73

80

74

42

81

58

79

86

60

61

73

Construct a 90​% confidence interval of the mean pulse rate for adult females.

___ bpm < mu < ___ bpm

​(Round to one decimal place as​ needed.)

Construct a 90​% confidence interval of the mean pulse rate for adult males.

___ bpm < mu < ___ bpm (Round to one decimal place as​ needed.)

Compare the results.

A. The confidence intervals do not​ overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.

B. The confidence intervals​ overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.

C. The confidence intervals​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

D. The confidence intervals do not​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

Solutions

Expert Solution

The t critical at = 0.10, df = n - 1 = 39 is 1.685

The Confidence Interval is given by ME

ME = t critical * s / sqrt(n)

____________________________________

For Females: = 73.98, s = 17.059, n = 40

ME = 1.685 * 73.98 / sqrt(40) = 4.54

Lower Limit = 67.98 - 4.54 = 69.44 = 69.4 (Rounded to 1 decimal place)

Upper Limit = 67.98 + 4.54 = 78.52 = 78.5 (Rounded to 1 decimal place)

The 90% Confidence interval is 69.4 < < 78.5

____________________________

For Males: = 67.2, s = 12.403, n = 40

ME = 1.685 * 12.403 / sqrt(40) = 3.3

Lower Limit = 67.2 - 3.3 = 63.9

Upper Limit = 67.2 + 3.3 = 70.5

The 90% Confidence interval is 63.9 < < 70.5

____________________________________________

(c) Comparing the results. Option C

The confidence intervals overlap, so it appears there is no significant difference in mean pulse rates between adult females and adult males.

___________________________________________

Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)2.

Males Females
# X Mean (x - mean)2 # X Mean (x - mean)2
1 85 67.180 317.552 1 79 73.980 25.200
2 71 67.180 14.592 2 94 73.980 400.800
3 52 67.180 230.432 3 59 73.980 224.400
4 58 67.180 84.272 4 65 73.980 80.640
5 53 67.180 201.072 5 54 73.980 399.200
6 62 67.180 26.832 6 83 73.980 81.360
7 52 67.180 230.432 7 76 73.980 4.080
8 79 67.180 139.712 8 86 73.980 144.480
9 53 67.180 201.072 9 88 73.980 196.560
10 61 67.180 38.192 10 57 73.980 288.320
11 72 67.180 23.232 11 38 73.980 1294.560
12 57 67.180 103.632 12 64 73.980 99.600
13 67 67.180 0.032 13 85 73.980 121.440
14 80 67.180 164.352 14 75 73.980 1.040
15 80 67.180 164.352 15 81 73.980 49.280
16 64 67.180 10.112 16 64 73.980 99.600
17 68 67.180 0.672 17 64 73.980 99.600
18 97 67.180 889.232 18 80 73.980 36.240
19 42 67.180 634.032 19 58 73.980 255.360
20 86 67.180 354.192 20 61 73.980 168.480
21 71 67.180 14.592 21 82 73.980 64.320
22 66 67.180 1.392 22 79 73.980 25.200
23 75 67.180 61.152 23 70 73.980 15.840
24 74 67.180 46.512 24 77 73.980 9.120
25 56 67.180 124.992 25 86 73.980 144.480
26 66 67.180 1.392 26 88 73.980 196.560
27 58 67.180 84.272 27 89 73.980 225.600
28 79 67.180 139.712 28 91 73.980 289.680
29 70 67.180 7.952 29 9 73.980 4222.400
30 65 67.180 4.752 30 96 73.980 484.880
31 61 67.180 38.192 31 69 73.980 24.800
32 98 67.180 949.872 32 90 73.980 256.640
33 55 67.180 148.352 33 85 73.980 121.440
34 63 67.180 17.472 34 79 73.980 25.200
35 56 67.180 124.992 35 75 73.980 1.040
36 56 67.180 124.992 36 55 73.980 360.240
37 65 67.180 4.752 37 102 73.980 785.120
38 73 67.180 33.872 38 74 73.980 0.000
39 81 67.180 190.992 39 79 73.980 25.200
40 60 67.180 51.552 40 73 73.980 0.960
Total 2687.00 5999.776 Total 2959.00 11348.976
Males Females
n 40 40
Sum 2687 2959
Average 67.2 73.98
SS(Sum of squares) 5999.776 11348.976
Variance = SS/n-1 153.8404 290.9994
Std Dev=Sqrt(Variance) 12.403 17.059

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