The length (in km) of a random sample of New Zealand (NZ) rivers that travel to the Pacific Ocean and the lengths (in km) of a random sample of New Zealand rivers that travel to the Tasman Sea are given in the table below. Do the data provide enough evidence to show on average that the rivers that travel to the Pacific Ocean are longer than the rivers that travel to the Tasman Sea?

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

Lengths of Rivers to Pacific Ocean (in km) 66 64 95 97 50 90 64 97 80 147 138 121 171 209 192 99 140 122 145 122 161 64 209 56 163 72

Lengths of Rivers to Tasman Sea (in km) 80 48 35 72 49 62 66 90 82 77 72 90 62 64 64 56 105 85 68 56 40 80 82 54 108 51 37

Part A.) HYPOTHESIS TEST P: Parameter

What is the correct parameter symbol and wording for population 1? Select an answer d p p n X N = Select an answer the length of a randomly selected New Zealand river that flows into the Pacific Ocean the mean length of 26 randomly selected New Zealand rivers that flow into the Pacific Ocean 26 randomly selected New Zealand rivers that flow into the Pacific Ocean the mean length of all New Zealand rivers that flow into the Pacific Ocean a randomly selected New Zealand river that flows into the Pacific Ocean What is the correct parameter symbol and wording for population 2? Select an answer p N p n X d = Select an answer the length of a randomly selected New Zealand river that flows into the Tasman Sea the mean length of 27 randomly selected New Zealand rivers that flow into the Tasman Sea a randomly selected New Zealand river that flows into the Tasman Sea 27 randomly selected New Zealand rivers that flow into the Tasman Sea the mean length of all New Zealand rivers that flow into the Tasman Sea H: Hypotheses

H0:H0: Select an answer - d X - X n - n N - N p - p p - p ? > < = km HA:HA: Select an answer n - n p - p X - X - p - p N - N d ? = > < km

A: Assumptions

Since Select an answer qualitative quantitative 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 were not two measurements taken on the same object, so these samples are Select an answer independent dependent

2. Is the value of11 known? ? Yes No

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 1-Proportion Z-Test 2-Sample T-Test T-Test 2-Proportion Z-Test Paired T-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 n - n p - p p - p d X - X - N - N = km

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 accept H fail to reject H reject H reject H . S: State a conclustion

• There Select an answer is is not significant evidence to conclude Select an answer the mean length of 26 randomly selected New Zealand rivers that flow into the Pacific Ocean the length of a randomly selected New Zealand river that flows into the Pacific Ocean a randomly selected New Zealand river that flows into the Pacific Ocean the mean length of all New Zealand rivers that flow into the Pacific Ocean 26 randomly selected New Zealand rivers that flow into the Pacific Ocean Select an answer is less than is equal to is more than differs from Select an answer 27 randomly selected New Zealand rivers that flow into the Tasman Sea the mean length of all New Zealand rivers that flow into the Tasman Sea the mean length of 27 randomly selected New Zealand rivers that flow into the Tasman Sea the length of a randomly selected New Zealand river that flows into the Tasman Sea a randomly selected New Zealand river that flows into the Tasman Sea .

Part B.) CONFIDENCE INTERVAL

N: Name the procedure

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

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

A % confidence interval for Select an answer - N - N n - n d X - X p - p p - p is ( km, km)

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 length of all New Zealand rivers that flow into the Pacific Ocean the length of a randomly selected New Zealand river that flows into the Pacific Ocean 26 randomly selected New Zealand rivers that flow into the Pacific Ocean the mean length of 26 randomly selected New Zealand rivers that flow into the Pacific Ocean a randomly selected New Zealand river that flows into the Pacific Ocean is between kmand km Select an answer more than less than Select an answer a randomly selected New Zealand river that flows into the Tasman Sea 27 randomly selected New Zealand rivers that flow into the Tasman Sea the mean length of 27 randomly selected New Zealand rivers that flow into the Tasman Sea the length of a randomly selected New Zealand river that flows into the Tasman Sea the mean length of all New Zealand rivers that flow into the Tasman Sea