Pearson Product-Moment Correlation and Hypothesis Test

A woman was interested in the relationship between the pollen count and the severity of her allergy symptoms. She developed a questionnaire that measured the severity of her symptoms with higher scores indicating worse allergy symptoms. She filled out and scored the questionnaire on 14 randomly selected days. She also had a friend record the pollen count for each of the days.

[Please refer to the attachment for the data to answer the following questions]

a. On the graph, draw a horizontal line representing the mean on the symptom questionnaire and a vertical line representing the mean pollen count. Then plot the data points for the sample of days in the study.

b. Calculate the Pearson product-moment correlation between pollen count and symptom severity.

c. Calculate a 90% confidence interval for the population correlation coefficient, ρ. Write one sentence summarizing what the confidence interval tells you.

d. Decide whether or not there is a relationship between the level of pollen in the air and the severity of this woman's allergy symptoms (Alpha= .05). Write one sentence explaining the result for a non-statistician.

e. Calculate the least squares regression line for predicting symptom severity from the pollen count. Plot the regression line on the graph above.

f. Describe the meaning of the coefficients in the regression equation. (Assume you are writing this for someone who is not very knowledgeable about math.)

g. Suppose the woman would like to predict how bad her symptoms will be this Saturday. She knows that the pollen count is forecast to be 80. What is your best estimate of her symptom score?

h. Estimate how bad her symptoms will be this Saturday and she knows that the pollen count is forecast to be 80 with a 95% confidence interval.

i. If the pollen count is forecast to be 80 but she has not shown ant symptoms, predict her symptom score with a 95% prediction interval.

j. Fill out the summary table below (see attached).