Question Instructions
- Answer all the questions provided.
- Show your calculations in detai...
Question Instructions
- Answer all the questions provided.
- Show your calculations in detail and explain the rationale of your answers thoroughly.
- Calculators are allowed.
1. A kitchenware company asked 10 customers the number of times they used the specialty cooking equipment they bought from the company in the last month:
4 6 8 6 7 2 1 8 12 10
A) Calculate the mean number of uses in the last month.
[5 marks]
B) Calculate the standard deviation. Make sure to show your calculations.
[15 marks]
2. A drilling company has estimated a 60% chance of striking oil for their new well. A detailed test has been scheduled. Historically, 40% of successful wells have had detailed test, and 10% of unsuccessful wells have had detailed test.
A) Given that this well has been scheduled for a detailed test, what is the probability that the well will be successful? Use Bayes’ Theorem.
[10 marks]
B) Would you say that the probability of successful drilling and the probability of having a detailed test are independent? Explain your answer using probabilities.
[10 marks]
3. Answer the following questions in no more than 3-4 lines for each one:
A) Why do you think investigating sample is more efficient for statistical control than investigating an entire population?
[5 marks]
B) What sample size is large enough to assume that the sampling distribution of proportion is normally distributed?
[5 marks]
C) Can 100% confidence level be used to determine a population parameter?
[5 marks]
D) What happens to confidence intervals when the confidence level is increased?
[5 marks]
4. A company claims that the average consumer buys 50 bars of chocolate in a calendar year Suppose a random sample of 100 consumers displayed the following statistics regarding the number of chocolate bars consumed in a year: X-bar=40, S=25.
A) What are the null and alternative hypotheses to determine if the number of chocolates consumed in a year is actually more or less than 50?
[5 marks]
B) What would be the value of the test statistic in this case?
[5 marks]
C) Considering that a confidence level of 5% for a normally distributed sample corresponds to a statistic score of ±1.96, what is your inference of the outcome in (B)?
[5 marks]
D) Explain briefly what are the Type I and Type II errors.
[5 marks]
5. A research group is trying to predict the performance of students on final exams based on the amount of time students study during the year. They use the following data:
SST = 110.00
SSR = 90.25
n = 200
A) Determine the coefficient of determination r2 and interpret its meaning.
[8 marks]
B) Determine the standard error of the estimate.
[7 marks]
C) How useful do you think this regression model is for predicting the performance of students on exams by the variation of the time spent studying?
[5 marks]
Answers: 1
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