Question

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

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

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

Call Europe 1 and Americas 2 in proceeding with analyses.

#8. Find the 98% confidence interval for the difference in mean number of cell phones for residents in Europe and the Americas. Fill in blank 1 to report the bounds of the 98% CI. Enter your answers as lower bound,upper bound with no additional spaces and rounding bounds to three decimals.

Blank #1: 98% confident that the true mean difference in number of cell phones per 100 residents in Europe and the Americas is between _____________and ___________________. In other words, the mean number of cell phones per 100 residents in Europe is anywhere from _________________ to _________________ more than the mean number of cell phones per 100 residents in the Americas.

#7. Is there enough evidence to show that the mean number of cell phones per 100 residents in countries of Europe is more than in countries of the Americas? Test at the 1% level.

Use the framework below to guide your work.

Hypotheses: :     Ho: mu1 = mu2; Ha: mu1 > mu2   

Blank #2: Test statistic = _________ (round to two decimal places)

Blank #3:  p-value = __________ (round to four decimal places)

Blank #4: Test decision: We decide to ___________ Ho (reject or do not reject)

Blank #5: Conclusion back into the words of problem: The evidence __________(favors or does not favor) that the mean number of cell phones per 100 residents is more for residents in Europe than it is for residents in the Americas.

Question 2 options:

Blank # 1
Blank # 2
Blank # 3
Blank # 4
Blank # 5

Answer 1

8) For Europe the sample size, mean, and standard deviation are

For America the sample size, mean, and standard deviation are

The standard error is

Now the difference, in means is

Now the number of degrees of freedom is 53+39-2=90

So for 98% confidence interval we have the critical value as

So, the margin of error is

Hence the interval is

7) The value of test static is

The test is right tailed test, with number of degrees of freedom is 90, the P-value is

So reject the null hypothesis as p-value is 0.0017<0.01

So, The evidence favors that the mean number of cell phones per 100 residents is more for residents in Europe than it is for residents in the Americas.