Question

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.

Answer 1

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