In: Statistics and Probability
Excel Questions
Q1. What is the sample mean of income?
Q2. What is the sample standard deviation of income? For questions 3 and 4, construct a 95% confidence interval for the average house price.
Q3. Enter the low end of the interval.
Q4. Enter the high end of the interval
Q5. The the typical household income in Indiana is $52,314. Suppose we want to test whether the people in this town earn a different amount on average. Find the p-value for this hypothesis test.
Q6. What is the highest confidence level at which you would reject the null hypothesis?
Q7. Suppose we want to test whether the two towns have the same unemployment rate. Find the p-value for this hypothesis test.
Q8. What is the highest confidence level at which you would reject the null hypothesis
Q9. Suppose we want to test whether runner 1 is faster than runner 2. Find the p-value for this hypothesis test.
Q10. What is the highest confidence level at which you would reject the null hypothesis
You run a small business with the following data for the last 100 days. Here is a summary for all of the variables:
Sales: Your revenue in dollars for the day.
Ads: The amount that you have spent on advertising.
Weekend: Equals 1 if it is on a weekend and 0 if not.
Holiday: Equals 1 if it is on a holiday and 0 if not
Run a regression with sales as your independent variable and ads, weekend and holiday as your dependent variables.
Q11. What is the p-value for the ads coefficient
Q12. What is the highest confidence level at which you would reject the null hypothesis that ads don't affect sales (use the dropdown list)?
Q13. What is the coefficient for ads?
Q14. Using this model, predict your sales for a day where you have spent $100 on ads, it is not a weekend and it is a holiday.
Run the same regression but with the natural logarithm of ads instead of ads.
Q15. What is the coefficient for ads now?
Q16. Which model performs better overall?
You run a store where you have data on the temperature outside and the amount that you spent on heating over the last 50 days.
Q17. What is the correlation between temperature and heating costs in this sample?
Q18. Find the test statistic for the hypothesis test for whether temperature and heating cost are correlated. (hint: look at CPA 14 part 1 for guidance)
Q19. What is the p-value for this hypothesis test? (hint: The t.dist functions require a positive value for x. Be sure to take the absolute value of the t-score using the abs function)
Q20. What is the highest confidence level at which you would reject the null hypothesis?
Income | House Price |
45724.50469 | 229669.22 |
64748.13922 | 321863.96 |
41116.40033 | 190247.32 |
49956.66181 | 221302.71 |
51784.69088 | 251299.13 |
47279.82381 | 197807.47 |
46923.55034 | 214079.92 |
58268.95352 | 277778.4 |
53413.40914 | 252928.77 |
63197.50762 | 315495.02 |
57404.75569 | 257250.09 |
80259.24003 | 420311.04 |
62592.35376 | 308995.72 |
47075.57529 | 207582.14 |
44444.71254 | 209651.72 |
56905.0827 | 278069.72 |
46043.99216 | 204041.9 |
45006.97844 | 179014.46 |
47630.56804 | 204106.32 |
49163.85754 | 218079.21 |
56087.47271 | 261491.14 |
41544.30524 | 178800.74 |
58855.80062 | 273530.03 |
62347.41604 | 325613.97 |
57244.67281 | 281427.6 |
61584.49916 | 290085.08 |
58997.79879 | 252881.31 |
64329.8906 | 305541.83 |
52245.42395 | 260409.85 |
1)
Income | |
Mean | 54213.03577 |
Standard Error | 1628.977904 |
Median | 53413.40914 |
Mode | #N/A |
Standard Deviation | 8772.31448 |
Sample Variance | 76953501.33 |
Kurtosis | 1.097222157 |
Skewness | 0.780953031 |
Range | 39142.8397 |
Minimum | 41116.40033 |
Maximum | 80259.24003 |
Sum | 1572178.037 |
Count | 29 |
1)
Mean | 54213.03577 |
2)
Standard Deviation | 8772.31448 |
3) and 4)
5)