Question

Data Set

Height	Weight	Age	Shoe Size	Waist Size	Pocket Change
64	180	39	7	36	18
66	140	31	9	30	125
69	130	31	9	25	151
63	125	36	7	25	11
68	155	24	8	31	151
62	129	42	6	32	214
63	173	30	8	34	138
60	102	26	6	25	67
66	180	33	8	30	285
66	130	31	9	30	50
63	125	32	8	26	32
68	145	33	10	28	118
75	235	44	12	40	60
68	138	43	8	27	50
65	165	55	9	30	22
64	140	24	7	31	95
78	240	40	9	38	109
71	163	28	7	32	14
68	195	24	10	36	5
66	122	33	9	26	170
53	115	25	7	25	36
71	210	30	10	36	50
78	108	23	7	22	75
69	126	23	8	24	175
77	215	24	12	36	41
68	125	23	8	30	36
62	105	50	6	24	235
69	126	42	9	27	130
55	140	42	8	29	14
67	145	30	8	30	50

Given the population mean for weight at 191.00 pounds, but no population standard deviation, using t = X-bar - µ/est. σx̄, and alpha .01, perfom the following seven-step process and contstruct the appropriate confidence intervals. Please write it out (fill-in the blanks) as detailed below.,

Step 1: Ho: u _ ____

               Ha : u _ ____

Step 2: Alpha level = ______

Step 3: Sampling distribution is ____________________

Step 4: Decision Rule—I will reject the Ho if the |_____| value falls at or beyond
the |_____| of _____, otherwise I will fail to reject

Step 5: Calculation—\_z_obs or t_obs__/ = ____

Step 6: Summary—Since the |____| of ____ falls at or beyond the |____| of ____, I therefore _________________.

Step 7: Conclusion—Since _________________ Ho occurred, I conclude that __________________________ in mean height value.

And the confidence intervals:

Answer 1

Solution

Preparatory Work

Data

i	xi (weight in lbs)
1	180
2	140
3	130
4	125
5	155
6	129
7	173
8	102
9	180
10	130
11	125
12	145
13	235
14	138
15	165
16	140
17	240
18	163
19	195
20	122
21	115
22	210
23	108
24	126
25	215
26	125
27	105
28	126
29	140
30	145

Summary of Excel Calculations

n =	30
µ0 =	191
Xbar =	150.9
s =	37.49147
tcal =	-5.85831
Given α =	0.01
tcrit =	2.756386
p-value	2.35E-06

Now, to work out the answer,

Part (a)

Step 1: Ho: µ = µ₀ = 191

            Ha : µ ≠191

Step 2: Alpha level = 0.01

Step 3: Sampling distribution is t with 29 degrees of freedom

Step 4: Decision Rule: I will reject the Ho if the |t_obs| value falls at or beyond
the upper 0.5% point of t₂₉, otherwise I will fail to reject

Step 5: Calculation: t_obs = - 5.858

Step 6: Summary: Since the | t_obs | of 5.858 falls beyond the |tcrit| of 2.756, I therefore reject the Ho.

Step 7: Conclusion: Since I reject the Ho,when Ho occurred, I conclude that 191 lbs is not in mean weight value.

Part (b)

Confidence intervals:

Back-up Theory

100(1 - α) % Confidence Interval for μ, when σ is not known is: Xbar ± (t_{n- 1, α /2})s/√n where

Xbar = sample mean, t_{n – 1, α /2} = upper (α /2)% point of

t-distribution with (n - 1) degrees of freedom, s = sample standard deviation and n = sample size.

Thus, 99% (given α = 0.01) Confidence Interval for μ is: 150.9 ± (2.756 x 37.491)/√30

= [132.033, 169.707]

[Note that the above CI does not contain 191 and hence Ho is rejected]