The Australian government would like to assess the impact of employment in different sectors on the number of days of parental leave taken by men. They ask 13 men employed in the public sector who had recently had a child, "how many days of parental leave have you taken?". They also ask 6 men in the private sector the same question. The public sector survey has a sample mean of 12.23 and standard deviation of 4, while the private sector survey has a sample mean of 30 and standard deviation of 5. What is the total number of individuals surveyed in this study?
The Australian government would like to assess the impact of employment in different sectors on the number of days of parental leave taken by men. They ask 13 men employed in the public sector who had recently had a child, "how many days of parental leave have you taken?". They also ask 6 men in the private sector the same question. The public sector survey has a sample mean of 12.23 and standard deviation of 4, while the private sector survey has a sample mean of 30 and standard deviation of 5.
What is the total number of individuals surveyed in this study?
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This question uses information from the previous question.
At 5% significance level, carry out a test to investigate if employment sector makes any difference to the amount of paternity leave taken.
You need to:
1. define new notation (if any),
2. briefly justify your testing procedure,
3. state the hypotheses,
4. calculate the test statistic and show steps of derivation,
5. use the p-value approach,
6. make a decision for the test and briefly explain.
by Bartleby ExpertThe Red Book is an Australian company that provides valuation information on the wholesale and retail prices of cars. Taking a random sample of used cars for sale from their database, sampling only for the same model and manufacture year of car, it is possible to model the relationship between the price of car (measured in thousands of dollars) and the number of kilometers it has been driven (measured in thousands of kilometers).
A least squares (LS) estimation is applied to estimate the regression model and some summary statistics are shown in the following table.
| Kilometers | Price | |
| ('000s) | ($, 000s) | |
| mean | 100.64 | 65.96 |
| var | 54.99 | 14.64 |
| cov | 20.66 | |
| sum of squares | 896084.17 | |
| sample size (n) | 88.00 | |
| sum of squared residuals | 598.38 |
Use this information to answer all the questions below.
(a) Fill the blanks in the regression table.
| table | estimate | s.e. | t | p-value |
| intercept | [a] | [b] | [c] | [d] |
| slope | [e] | [f] | [g] | [h] |
In your answer, you may arrange the values as in the above output table or simply write [a]=XXX, ..., [h]=XXX.
(b) What is the value of R2 (R-squared)
(c) What is the underlying null hypothesis for β1 (beta_1) from the t-statistic in the Table of question (a)?
(d) What is the underlying alternative hypothesis for β1(beta_1) from the p-values in the Table of question (a)?
(e) Compute the 90% confidence interval for β1 (beta_1) and explain its interpretation. Show the steps of calculation.
(f) Carry out a test to investigate if low kilometers are associated with high prices at the 1% significance level. You need to
(1) define new notation (if any),
(2) briefly justify your testing procedure,
(3) state the hypotheses,
(4) calculate the test statistic and show your calculation steps,
(5) use the p-value approach,
(6) make decision for the test and briefly explain.
by Bartleby Expert
