Question

The number of cell phones per 100 residents in countries in Europe is given in table #1 for the year 2010. The number of cell phones per 100 residents in countries of the Americas is given in table #2 also for the year 2010 ("Population reference bureau," 2013).

Table #1: Number of Cell Phones per 100 Residents in Europe

100	76	100	130	75	84
112	84	138	133	118	134
126	188	129	93	64	128
124	122	109	121	127	152
96	63	99	95	151	147
123	95	67	67	118	125
110	115	140	115	141	77
98	102	102	112	118	118
54	23	121	126	47

Table #2: Number of Cell Phones per 100 Residents in the Americas

158	117	106	159	53	50
78	66	88	92	42	3
150	72	86	113	50	58
70	109	37	32	85	101
75	69	55	115	95	73
86	157	100	119	81	113
87	105	96

Is there enough evidence to show that the mean number of cell phones in countries of Europe is more than in countries of the Americas? Test at the 1% level.

(i) Let μ₁= mean number of cell phones per 100 residents in countries of Europe. Let μ₂ = mean number of cell phones per 100 residents in countries of the Americas. Which of the following statements correctly defines the null hypothesis H_O?

A.  μ₁ + μ₂= 0

B.  μ₁ – μ₂< 0 (μ₁ < μ₂)

C.  μ₁ − μ₂ > 0 (μ₁ > μ₂)

D.  μ₁ − μ₂ = 0 (μ₁ = μ₂)

Enter letter corresponding to correct answer

(ii)   Let μ₁= mean number of cell phones per 100 residents in countries of Europe. Let μ₂ = mean number of cell phones per 100 residents in countries of the Americas. Which of the following statements correctly defines the alternate hypothesis H_A?

A.  μ₁ − μ₂ > 0 (μ₁ > μ₂)

B.  μ₁ – μ₂< 0 (μ₁ < μ₂)

C.   μ₁ − μ₂ = 0 (μ₁ = μ₂)

D.  μ₁ + μ₂= 0

(iii) Enter the level of significance α used for this test:

(iv)  For sample from population with mean = μ1 :          Determine sample mean x¯1 and sample standard deviation s1variant

(v)  For sample from population with mean = μ2 :       Determine sample mean x¯2 and sample standard deviation s2

(vi) Determine degrees of freedom df :

(vii) Determine test statistic:

Enter value in decimal form rounded to nearest thousandth.  

(viii) Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth.  

(ix) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Accept H_o

B. Fail to reject H_o

C. Reject H_o

D. Accept H_A

(x) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean number of cell phones in countries of Europe is more than in countries of the Americas.

B. The result is not statistically significant at .01 level of significance. There is not enough evidence to support the claim that the mean number of cell phones in countries of Europe is more than in countries of the Americas.

C. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean number of cell phones in countries of Europe is more than in countries of the Americas.

D. The result is statistically significant at .01 level of significance. There is not enough evidence to support the claim that the mean number of cell phones in countries of Europe is more than in countries of the Americas.

Answer 1

NULL HYPOTHESIS H0: μ1 − μ2 = 0 (μ1 = μ2)

ALTERNATIVE HYPOTHESIS Ha:   μ1 − μ2 > 0 (μ1 > μ2)

alpha= 0.01

(iv)  For sample from population with mean = μ1 :          Determine sample mean x¯1 = 108.1509 and sample standard deviation s1= 29.96

(v)  For sample from population with mean = μ2 :       Determine sample mean x¯2 =87.2051

and sample standard deviation s2= 35.15

(vi) Determine degrees of freedom df : 90

(vii) Determine test statistic: 3.078

(viii) Determine and enter p-value corresponding to test statistic is 0.003

ix) P value<0.01 level of significance

Decision: Reject Ho

x) The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean number of cell phones in countries of Europe is more than in countries of the Americas. OPTION C