Question

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]

Answer 1

Let x be a random variable representing the price of a Congo-imported black diamond. Let the higher price be p. Then,

P(x < p) = P(x < (p - mean)/sd) = P(x < (p - 60,430)/21,958.08) = P(z < 2)

Therefore,

(p - 60,430)/21,958.08 = 2

p - 60,430 = 2 x 21,958.08 = 43,916.16

p = 34,916.16 + 60,430 = 104.346.16

Therefore, The required price is $104,346.16

Step-by-step explanation: