Statistics Assignment

1. Professor is trying to buy a house, but homes in his target area are commonly selling for over list price. He collects a simple random sample of recent home sales in his area and computes for each the percent over list price each sale represents. This data is recorded in the POL variable (as decimals: e.g. 0.13 = 13%. Negative numbers indicating sale price below list price).

a)[5] Decide, using StatCrunch to help, whether or not the distribution is approximately normal.

b)[10] Professor wants to make an offer on a house that has a listing price of $300,000. Use a normal model to determine an offer price for Professor which would put it in the 80^th percentile in terms of its percent over asking price. Round to the nearest $1,000. [Remember to show all work and include any StatCrunch output.]

1. [10] Researchers are attempting to determine if a new drug can reduce the average recovery time from the common cold. They split, via random assignment, a random sample of common cold sufferers into treatment and placebo groups and measure recovery time. The data are presented in the CCtreatment and CCcontrol variables. Is the improvement shown in the treatment group statistically significant? Use a hypothesis test to decide.
2. Professor suspects less than half of the flowering weeds in his yard are dandelions. To decide the issue, he maps out his yard into squares approximately 3 feet by 3 feet, then randomly selects 10 such squares and notes all the flowering weeds found in each. His data is collected in the weeds variable.

a)[5] What type of sampling method did Professor Herning use? Explain.

b)[5] Use StatCrunch to make both an appropriate tabular and an appropriate graphical summary of the data.

c)[10] Assuming the data represents a simple random sample of the flowering weeds in Professor’s yard, do they provide convincing evidence for Professor’s suspicion? Use an appropriate inference method of your choice from our class to decide.

1. NVCC’s Office of Institutional Research (OIR) decides to determine if the proportion of self-reported minority students enrolled in NVCC’s MTH 245 classes this semester is different from the proportion enrolled in MTH 264. The variables class and mstatus record class and minority status from a randomly chosen selection of 100 students.

a)[5] Create a contingency table to summarize the data. Which group has a higher proportion of minority students?

b)[10] Create a confidence interval for the difference between the proportions of MTH 245 and MTH 264 students who self-report minority status. Does your confidence interval suggest the difference is statistically significant?

1. Professor gives a diagnostic test on the first day of his precalculus classes. He wants to know if there is a correlation between diagnostic scores and final exam scores. The PCdiagnostic and PCexam variables contain the scores for a random sample of his precalculus students (each row representing the same student in both variables).

a)[5] Use StatCrunch to perform a linear regression for predicting the exam score from the diagnostic score. Paste the output statistics page as well as the scatter plot with least squares regression line.

b)[5] State and interpret the slope and R² value of the model in context.

c)[5] What is the predicted exam score for a student scoring 73 on the diagnostic?

d)[5] Assuming the conditions for inference are satisfied (do not use the four step procedure), does the sample provide strong evidence that the correlation between the diagnostic test score and the exam score is positive? Explain, using the appropriate part(s) of the StatCrunch output.