The number of cell phones per 100 residents in randomly selected countries of the Americas is given in the table below for a particular year. The number of cell phones per 100 residents in randomly selected countries in Europe is also given in the table below for the same year. Is there enough evidence to show that the mean number of cell phones in countries in the Americas is less than in countries in Europe?

a) Test at the 4% level. b) Compute a 92% confidence interval for the difference.

Number of Cell Phones in countries of the Americas (in cell phones per 100 residents) 50 105 58 32 96 100 87 3 78 109 69 117 66 37 158 53 115 86 95 85 92 42 75 86 55 150 157 50 113 119 159 101 73 106 88

Number of Cell Phones in countries in Europe (in cell phones per 100 residents) 115 102 133 84 129 112 95 118 95 141 121 67 109 152 130 47 123 118 127 134 110 112 64 98 118 124 54 63 75 140 77 125 96 115 151 121 126

Part A.) HYPOTHESIS TEST P: Parameter

What is the correct parameter symbol and wording for population 1? Select an answer p p d n X N = Select an answer 35 randomly selected countries of the Americas the mean number of cell phones per 100 residents of all countries of the Americas the mean number of cell phones per 100 residents of 35 randomly selected countries of the Americas a randomly selected country of the Americas the number of cell phones per 100 residents of a randomly selected country of the Americas What is the correct parameter symbol and wording for population 2? Select an answer N n d X p p = Select an answer the mean number of cell phones per 100 residents of all countries in Europe 37 randomly selected countries in Europe the number of cell phones per 100 residents of a randomly selected country in Europe the mean number of cell phones per 100 residents of 37 randomly selected countries in Europe a randomly selected country in Europe H: Hypotheses

H0:H0: Select an answer N - N X - X d p - p - p - p n - n ? = > < cell phones per 100 residents HA:HA: Select an answer N - N p - p p - p d X - X n - n - ? > < = cell phones per 100 residents

A: Assumptions

Since Select an answer quantitative qualitative information was collected from each object, we need to check the following conditions:

Check all that apply.

• x1>10x1>10 and x210x210
• n1x110n1-x110 and n2x210n2-x210
• n120n1n120n1 and n220n2n220n2
• The samples are independent
• The samples are dependent
• Normal population of differences or at least 30 pairs of data
• Normal populations or n130n130 and n230n230
• no outliers in the differences
• no outliers for each group
• is unknown for each group
• is known for each group

Check those assumptions: 1. There Select an answer were not were two measurements taken on the same object, so these samples are Select an answer independent dependent

2. Is the value of11 known? ? No Yes

Is the value of22 known? ? No Yes

3. Are there any outliers in data set 1? Select an answer No, the modified boxplot of the differences shows no outliers No, the modified boxplot of this data set shows no outliers Yes, the modified boxplot of the differences shows outliers Yes, the modified boxplot of this data set shows outliers Yes, the normal probability plot of this data set shows outliers No, the normal probability plot of this data set shows no outliers Yes, the histogram of this data set shows outliers No, the histogram of this data set shows no outliers

Are there any outliers in data set 2? Select an answer No, the modified boxplot of the differences shows no outliers No, the modified boxplot of this data set shows no outliers Yes, the modified boxplot of the differences shows outliers Yes, the modified boxplot of this data set shows outliers Yes, the normal probability plot of this data set shows outliers No, the normal probability plot of this data set shows no outliers Yes, the histogram of this data set shows outliers No, the histogram of this data set shows no outliers

4.n1n1 = which is ? < Is it reasonable to assume that population 1 is normally distributed? Select an answer Not necessary to check since the sample size is at least 30. Not necessary to check since the sample size is less than 30. Yes since the normal probability plot of the differences is roughly linear with no outliers. Yes since the normal probability plot of the differences is roughly bell-shaped with no outliers. No, since the normal probability plot of the differences is not roughly linear. No, since the normal probability plot of the differences is not roughly bell-shaped. Yes, since the normal probability plot of data is roughly linear with no outliers. No, since the normal probability plot of the list of data is not roughly linear with no outliers.

n2n2 = which is ? <

Is it reasonable to assume that population 2 is normally distributed?

Select an answer Not necessary to check since the sample size is at least 30. Not necessary to check since the sample size is less than 30. Yes since the normal probability plot of the differences is roughly linear with no outliers. Yes since the normal probability plot of the differences is roughly bell-shaped with no outliers. No, since the normal probability plot of the differences is not roughly linear. No, since the normal probability plot of the differences is not roughly bell-shaped. Yes, since the normal probability plot of data is roughly linear with no outliers. No, since the normal probability plot of the list of data is not roughly linear with no outliers.

N: Name the test

The conditions are met to use a Select an answer 2-Sample T-Test T-Test Paired T-Test 2-Proportion Z-Test 1-Proportion Z-Test . T: Test Statistic

The symbol and value of the random variable on this problem are as follows:

Round value to 2 decimal places Select an answer p - p n - n N - N X - X p - p d - = cell phones per 100 residents

Set up the formula of the test statistic with numbers rounded to 2 decimal place: t=x1x2((s21n1)+(s22n2))=t=x1-x2((s12n1)+(s22n2))=

(( - )) / ( ^2^2 / )+()+( ^2^2 / ))))

Final answer from technology to 2 decimal places:

tt = O: Obtain the P-value

Report the final answer to 4 decimal places.

It is possible when rounded that a p-value is 0.0000 P-value = M: Make a decision

Since the p-value ? > < = , we Select an answer fail to reject H reject H fail to reject H reject H accept H . S: State a conclustion

• There Select an answer is is not significant evidence to conclude Select an answer a randomly selected country of the Americas the mean number of cell phones per 100 residents of all countries of the Americas the mean number of cell phones per 100 residents of 35 randomly selected countries of the Americas 35 randomly selected countries of the Americas the number of cell phones per 100 residents of a randomly selected country of the Americas Select an answer is more than is less than differs from is equal to Select an answer the mean number of cell phones per 100 residents of 37 randomly selected countries in Europe 37 randomly selected countries in Europe the mean number of cell phones per 100 residents of all countries in Europe the number of cell phones per 100 residents of a randomly selected country in Europe a randomly selected country in Europe .

Part B.) CONFIDENCE INTERVAL

N: Name the procedure

Select an answer 2-Sample T-Interval T-Interval 1-Proportion Z-Interval Paired T-Interval 2-Proportion Z-Interval

I: Interval estimate (round endpoints to 2 decimal place(s))

A % confidence interval for Select an answer p - p p - p - d n - n X - X N - N is ( cell phones per 100 residents, cell phones per 100 residents)

C: Conclusion in context

• If your interval above contains 0, then we don't care about the interpretation since there was no significant difference in these means. In this case, just enter "0" for each of the endpoints below (the program won't let you leave them blank). On your homework guide you should write "We don't interpret the interval when there is no evidence of a difference"
• We are % confident that Select an answer the mean number of cell phones per 100 residents of 35 randomly selected countries of the Americas the mean number of cell phones per 100 residents of all countries of the Americas the number of cell phones per 100 residents of a randomly selected country of the Americas 35 randomly selected countries of the Americas a randomly selected country of the Americas is between cell phones per 100 residentsand cell phones per 100 residents Select an answer less than more than Select an answer 37 randomly selected countries in Europe the mean number of cell phones per 100 residents of all countries in Europe a randomly selected country in Europe the number of cell phones per 100 residents of a randomly selected country in Europe the mean number of cell phones per 100 residents of 37 randomly selected countries in Europe