Statistics-Find the upper critical values based on F distribution

| March 29, 2017

Question
QMB 3200

Homework #4
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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
future weekend guest bills to test the manager’s claim.
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 under-filling or overfilling is occurring. If the sample data lead to a conclusion of
under-filling 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) CarpetPlace salespersons average $5,000 per week in sales. Steve Jobs, the firm’s vice
president, proposes a new compensation plan with selling incentives. Steve hopes that the
results of a trial selling period will enable him to conclude that the new compensation plan
increases the average sales per salesperson.
a) Develop the appropriate null and alternative hypotheses.
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) Department of Labor reported the average hourly earnings for production workers to be
$15.23 per hour in 2001. A sample of 75 production workers during 2003 showed a sample
mean of $15.86 per hour. Assuming the population standard deviation is $1.50, can we
conclude that an increase occurred in the mean hourly earnings since 2001? Use α = .05.
5) ABC Securities Firm paid out record year-end bonuses of $150,000 per employee for 2005.
Suppose we would like to take a sample of employees at the ABC Securities firm to see
whether the mean year-end bonus is different from the reported mean of $150,000 for the
population.
a) State the null and alternative hypotheses you would use to test whether the year-end
bonuses paid by ABC Securities were different from the population mean.
b) Suppose a sample of 40 employees showed a sample mean year-end bonus of $130,000.
Assume a population standard deviation of $30,000 and compute the p- value.
c) With a .05 as the level of significance, what is your conclusion?
d) Repeat the preceding hypothesis test using the critical value approach.
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6) Find t values from t distribution tables for the following:
a) Area in the upper tail = 0.025 and Sample Size = 101
b) Area in the upper tail = 0.01 and Sample Size = 83
c) Area in the upper tail = 0.05 and Sample Size = 67
d) Area in the lower tail = 0.005 and Sample Size = 18
e) Area in the lower tail = 0.10 and Sample Size = 26
7) Find the chi-square values from chi-square distribution tables.
a) χ20.005 with Sample Size = 101
b) χ20.10 with Sample Size = 30
c) χ20.05 with Sample Size = 16
d) χ20.995 with Sample Size = 19
e) χ20.99 with Sample Size = 96
8) Find the upper critical values based on F distribution tables (given, variance of sample 1 is
greater than variance of sample 2). Alpha and Sample Sizes are as follows:
a) α = .05 with n1 = 6 and n2 = 11
b) α = .025 with n1 = 21 and n2 = 26
c) α = .01 with n1 = 61 and n2 = 61
d) α = .10 with n1 = 9 and n2 = 25
e) α = .025 with n1 = 31 and n2 = 23

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