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8STT117 : Statistics and Probability

Homework

Date due on October 27^th, 2023 before 5 pm.

This is an individual homework

Write your answers on the first page of this document

Question 1 6 points

i) If H₀ is false and has been rejected, what type of error has been made?

a) Type I error

b) Type II error

c) No error

d) Not enough information to answer

ii) When H₀ is true and α is 0.01, what is the probability of making a type I error?

iii) YES OR NO. A clinician declares that a patient has schizophrenia with a probability of 0.01. Is this clinician committing a type II error towards this patient?

iv) TRUE OR FALSE: The sampling distribution is defined as the theoretical distribution of all the statistical values (e.g., the mean) calculated on an infinite number of samples of the same size (n) taken at random from the same population.

v) TRUE OR FALSE: The standard error is the standard deviation of a sampling distribution.

vi) YES OR NO. Is it true that the standard error of the statistic decreases as n increases?

Question 2 3 points

Air pollution in 41 American cities is studied using the variable y, measuring the volume of SO2 in the air in micrograms per m3, as a function of the mean annual temperature x, expressed in degrees Fahrenheit. The following results are given:

i) Calculate the linear correlation coefficient of X and Y.

ai) Give the equation of the regression line of Y on X.

iii) What value of Y would you predict for a city where the mean temperature is 60 °F?

Question 3 3 points

Assume you have noted the following prices for paperback books and the number of pages that each book contains.

i) Compute the coefficient of determination.

ii) Compute the correlation coefficient between the price and the number of pages.

iii) Test to see if x and y are related. Use α = 0.10.

Question 4 1 point 

Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. Compute the test statistic.

Question 5 1 point

The following information was obtained from matched samples.

What is the 95% confidence interval for the difference between the two population means?

a. -3.776 to 1.776

b. -3.483 to 1.483

c. -3.299 to 1.299

d. -3.571 to 1.571

e. None of these answers

Question 6 1 point

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered.

Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use α = 0.05. We assume that both populations follow the normal distribution.

a. -9.121 to -2.879

b. -8.987 to -3.013

c. -11.228 to -0.772

d. -8.507 to -3.493

e. -10.199 to -1.801

e. None of these answers