Below are the poverty rates and murder rates of six states, along with the mean

Question

Below are the poverty rates and murder rates of six states, along with the mean and SD of each variable. Test the null hypothesis that there is no relationship between poverty rate and murder rate at the .05 significance level.

Research Hypothesis: There is a relationship between states’ poverty levels and their murder levels.
Null Hypothesis: There is no relationship between states’ poverty levels and their murder levels.

The comparison distribution is a t-distribution.

1. How many df does the Comparison Distribution have?

2. Critical Value(s):

3. Calculate a Pearson’s correlation coefficient for these data (r)

(Give your answer to at least 3 places past the decimal point)

4. Calculate t to perform a hypothesis test of this correlation

(Give your answer to at least 3 places past the decimal point)

5. Draw A Conclusion (Explain what your decision in Step 5 tells us about the topic being studied in terms that someone who doesn’t know anything about significance tests can understand. Make sure you talk about the poverty rates and murder rates of states, and do not use the words “significant”, “null hypothesis” “critical value” etc. Include the direction of the effect.)

6. Calculate the proportion of the variance in murder rate associated with poverty rate in this sample.
(give your answer to at least 3 places past the decimal point)

7. Explain, in words, what the proportion you calculated in the last question means? (hint: Don’t give the size of the effect according to Cohen. Explain what the value you just calculated means in terms of states’ poverty and murder rates.) Hint: Review the lecture video from 41:40 to 45:10

State Poverty Rate Muder Rate New Hampshire 9.2 1.3 Mississippi 21.9 8.0 Delaware 13.0 5.9 Wyoming 10.6 3.4 Michigan 16.2 6.0 Montana 15.2 3.5 Mean 14.35 4.683 SD 4.154 2.187

Explanation / Answer

1. The df is 4 (n-2=6-2=4).

2. The critical value is 0.811.

3. The Pearson correlation coefficient is 0.863.

4. The value of t is -8.574.

Please post the other questions separately as we are supposed to answer just one question or four sub parts of a question.

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