Assignment 1
Statistics for Business and Economics II,
ECO 204, Section: 3
Course Instructor: Asiya Siddica (ASC)
Date of Submission: 17th November, Wednesday, 2021
Chapter 9: Hypothesis Testing
1. The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a
weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total
charges for guest bills have been increasing in recent months. The accountant will use a
sample of weekend guest bills to test the manager’s claim.
𝑯𝟎 : 𝝁 ≥ 𝟔𝟎𝟎
𝑯𝟎 : 𝝁 ≤ 𝟔𝟎𝟎
𝑯𝒂 : 𝝁 < 𝟔𝟎𝟎
𝑯𝒂 : 𝝁 > 𝟔𝟎𝟎
𝑯𝟎 : 𝝁 = 𝟔𝟎𝟎
𝑯𝒂 : 𝝁 ≠ 𝟔𝟎𝟎
a. Which form of the hypotheses should be used to test the manager’s claim? Explain.
b. What conclusion is appropriate when H0 cannot be rejected?
c. What conclusion is appropriate when H0 can be rejected?
2. A production line operation is designed to fill cartons with laundry detergent to a mean
weight of 32 ounces. A sample of cartons is periodically selected and weighed to
determine whether underfilling or overfilling is occurring. If the sample data lead to a
conclusion of underfilling or overfilling, the production line will be shut down and
adjusted to obtain proper filling.
a. Formulate the null and alternative hypotheses that will help in deciding whether to
shut down and adjust the production line.
b. Comment on the conclusion and the decision when H0 cannot be rejected.
c. Comment on the conclusion and the decision when H0 can be rejected.
3. Suppose a new production method will be implemented if a hypothesis test supports the
conclusion that the new method reduces the mean operating cost per hour.
a. State the appropriate null and alternative hypotheses if the mean cost for the
current production method is $220 per hour.
b. What is the Type I error in this situation? What are the consequences of making this
error?
c. What is the Type II error in this situation? What are the consequences of making
this error?
4. Consider the following hypothesis test: A sample of 40 provided a sample mean of 26.4.
The population standard deviation is 6.
H0: μ ≤ 25
Ha: μ > 25
a. Compute the value of the test statistic.
b. What is the p-value?
c. At α = .01, what is your conclusion using p value approach?
d. What is the rejection rule using the critical value? What is your conclusion?
5. Consider the following hypothesis test
H0: μ = 22
Ha: μ ≠ 22
A sample of 75 is used and sample mean, and the population standard deviation are 23 &
10.
a. Compute the value of the test statistic.
b. What is the p-value?
c. At α = .01, what is your conclusion using p value approach?
d. What is the rejection rule using the critical value? What is your conclusion?
6. Consider the following hypothesis test: A sample of 48 provided a sample mean 𝑥̅ = 17
and a sample standard deviation s = 4.5.
H0: μ = 18
Ha: μ ≠ 18
a. Compute the value of the test statistic.
b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value.
c. At α = .05, what is your conclusion?
d. What is the rejection rule using the critical value? What is your conclusion?
7. Speaking to a group of analysts in January 2006, a brokerage firm executive claimed that
at least 70% of investors are currently confident of meeting their investment objectives.
A UBS Investor Optimism Survey, conducted over the period January 2 to January 15,
found that 67% of investors were confident of meeting their investment objectives
(CNBC, January 20, 2006).
a. Formulate the hypotheses that can be used to test the validity of the brokerage firm
executive’s claim.
b. Assume the UBS Investor Optimism Survey collected information from 300 investors.
What is the p-value for the hypothesis test?
c. At α = .05, should the executive’s claim be rejected?
Chapter 10: Inference about two population mean and proportions
8. The average expenditure on Valentine’s Day was expected to be $100.89 (USA Today,
February 13, 2006). Do male and female consumers differ in the amounts they spend? The
average expenditure in a sample survey of 40 male consumers was $135.67, and the average
expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys,
the standard deviation for male consumers is assumed to be $35, and the standard deviation
for female consumers is assumed to be $20.
a. What is the point estimate of the difference between the population mean expenditure for
males and the population mean expenditure for females?
b. At 99% confidence, what is the margin of error?
c. Develop a 99% confidence interval for the difference between the two population mean?
d. Conduct a hypothesis test at a 5% level of significance, does male and female consumers
differs in the amount they spend. What is your conclusion regarding accepting or rejecting
Null hypothesis?
9. Consider the following hypothesis test.
𝐻0 = 𝜇1 − 𝜇2 = 0
𝐻𝑎 = 𝜇1 − 𝜇2 ≠ 0
The following results are from independent samples taken from two populations.
a)
b)
c)
d)
Sample 1
Sample 2
𝒏𝟏 = 𝟑𝟓
𝒏𝟐 = 𝟒𝟎
̅̅̅
𝒙𝟏 = 𝟏𝟑. 𝟔
̅̅̅
𝒙𝟐 = 𝟏𝟎. 𝟏
𝒔𝟏 = 𝟓. 𝟐
𝒔𝟐 = 𝟖. 𝟓
What is the value of the test statistic?
What is the degrees of freedom for the t distribution?
What is the p-value?
At α = .05, what is your conclusion?
Chapter 12: Goodness of Fit
10. The National Sleep Foundation used a survey to determine whether hours of sleeping
per night are independent of age (Newsweek, January 19, 2004). The following show the
hours of sleep on weeknights for a sample of individuals aged 49 and younger and for a
sample of individuals age 50 and older.
Age
49 or
younger
50 or older
Fewer than
6
38
6 to 6.9
Hours of Sleep
7 to 7.9
60
77
65
240
36
57
75
92
260
8 or more
Total
a. Conduct a test of independence to determine whether the hours of sleep on weeknights
are independent of age. Use α = .05. What is the p-value, and what is your conclusion?
b. What is your estimate of the percentage of people who sleep fewer than 6 hours, 6 to 6.9
hours, 7 to 7.9 hours, and 8 or more hours on weeknights?