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Stat 2103 - Take Home Final Exam due Wednesday Dec 12 11:59pm
The data for these problems are on the Excel sheet for Week 15 on Canvas.
You can show your work in the Excel sheet. Rename the Excel file with your last name and upload it via
the Canvas link on Week 15.
Type your answers on this sheet. Upload it before midnight on Wed Dec 12.
(1) (6 pts) An auto loan company is interested in the difference in credit history for young and old borrowers.
A sample of 1000 loans from younger borrowers found 3.0% defaulted and 500 loans from older
borrowers found 6.0% defaulted.
a. Construct a 95% confidence interval around the difference default rates for old and young
borrowers. What are the lower and upper bounds of this confidence interval?
The 95% confidence interval of the difference in default rates for old and young is:
𝟎. 𝟎𝟎𝟔𝟕 < 𝒑𝒐𝒍𝒅 − 𝒑𝒚𝒐𝒖𝒏𝒈 < 𝟎. 𝟎𝟓𝟑𝟑
b. Is there a statistically significant difference in the default rates between old and young
borrowers at the 5% significance level?
Since the 95% confidence interval does not include 0, at 5% significance level, there is
statistically significant difference in the default rates between old and young borrowers.
(2) (9 pts) Use the data on the sheet “FishWt”. This data was sampled from a certain population of fish. A
biologist wants to test the research hypothesis that this fish population has a mean weight below 10
oz. Test the research hypothesis that sales increase during the campaign at the 5% significance level.
a. What are the null and alternative hypotheses?
Null hypothesis:
Alternative hypothesis:
𝐇𝟎 : 𝛍𝐰𝐞𝐢𝐠𝐡𝐭 = 𝟏𝟎
𝐇𝐚 : 𝛍𝐰𝐞𝐠𝐡𝐭 < 𝟏𝟎
b. What is the appropriate p-value?
The p-value of the left-tailed t-test is 0.0058
c. Using this data, can the biologist infer at the 1% significance level that the fish population has
an average weight below 10 oz? State your conclusion.
At 1% significance level, the p-value (0.0058) is less than alpha (i.e. 𝜶 = 𝟎. 𝟎𝟏). We reject the
null hypothesis and accept the alternative hypothesis. In conclusion, there is sufficient
evidence to support the alternative hypothesis that the mean weight is less than 10 oz.
(3) (15 pts) Use the data on the sheet “Bedrooms” to create a simple regression model. Use Price as the
dependent (Y) variable and Bedrooms as the independent (X) variable.
a. What is the slope and intercept for this model? What the units of the slope?
The slope is: ...