Question
In: Statistics and Probability
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can...
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed within 15 minutes or less. If more time is required, a premium rate is charged. With a sample of 35 surveys, a population standard deviation of 4 minutes, and a level of significance of .01, the sample mean will be used to test the null hypothesis H0: μ ≤15.
a. What is your interpretation of the Type II error for this problem? What is its impact on the firm?
b. What is the probability of making a Type II error when the actual mean time is μ =17 minutes?
c. What is the probability of making a Type II error when the actual mean time is μ = 18 minutes?
d. Sketch the general shape of the power curve for this test
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Solutions
orchestra answered 2 years agoRelated Solutions
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can...
Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. Suppose a sample of 35 surveys produces
the data in the Microsoft Excel Online file below. Use a known
σ = 3.9 minutes. Is the premium rate justified?
Hypothesis Test about a Population Mean:
Formulas
Sigma Known Case
Sample Size...
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can...
Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. A sample of 35 surveys provided a mean
time of 17 minutes. Based upon past studies, the population
standard deviation is assumed known with σ=4. Is the premium rate
justified?
What is the critical value, using a = .01 (to...
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can...
Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed within an
average time of 15 minutes or less. If more time is required, a
premium rate is charged.
The testable hypotheses in this situation are ?0:?=15H0:μ=15 vs.
??:?>15Ha:μ>15
1. Identify the consequences of making a Type I
error.
A. The company charges the customer the premium
rate when they should.
B. The company does not charge the customer the
premium rate...
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can...
Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. Suppose a sample of 35 surveys produces
the data in the Microsoft Excel Online file below. Use a known
σ = 3.3 minutes. Is the premium rate justified?
Call Time (minutes)
20.3
13.7
16.2
18.1
13.5
17.3
14.6
17.4
18.5...
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can...
Fowle Marketing Research, Inc., bases charges to a client on the
assumption that telephone surveys can be completed in a mean time
of 15 minutes or less. If a longer mean survey time is necessary, a
premium rate is charged. Suppose a sample of 35 surveys produces
the data in the Microsoft Excel Online file below. Use a known
σ = 3.7 minutes. Is the premium rate justified?
Formulate the null and alternative hypotheses for this
application.
H0: μ _________greater...
A market research firm conducts telephone surveys with a 43% historical response rate. a. What is...
A market research firm conducts telephone surveys with a 43%
historical response rate.
a. What is the probability that in a new sample
of 400 telephone numbers, at least 160 individuals will cooperate
and respond to the questions? In other words, what is the
probability that the sample proportion will be at least 160/400 =
0.4?
Calculate the standard error to 4 decimals.
Calculate the probability to 4 decimals, showing your steps along
the way.
P( ≥ ) = P(z ≥ )...
A market research firm conducts telephone surveys with a 47% historical response rate. If 75 individuals...
A market research firm conducts telephone surveys with a 47%
historical response rate. If 75 individuals are contacted, find the
probability that 36 or less of them will cooperate and respond to
the survey questions.
A marketing research professor is conducting a telephone survey and needs to contact at least 160...
A marketing research professor is conducting a telephone survey
and needs to contact at least 160 wives, 140 husbands, 110 single
adult males, and 120 single adult females. It costs $2 to make a
daytime call and $4 (because of higher labor costs) to make an
evening call. The table shown below lists the expected results. For
example, 10% of all daytime calls are answered by a single male,
and 15% of all evening calls are answered by a single...
A marketing research professor is conducting a telephone survey and needs to contact at least 160...
A marketing research professor is conducting a telephone survey
and needs to contact at least 160 wives, 140 husbands, 110 single
adult males, and 120 single adult females. It costs $2 to make a
daytime call and $4 (because of higher labor costs) to make an
evening call. The table shown below lists the expected results. For
example, 10% of all daytime calls are answered by a single male,
and 15% of all evening calls are answered by a single...
A marketing research professor is conducting a telephone survey and needs to contact at least 160...
A marketing research professor is conducting a telephone survey
and needs to contact at least 160 wives, 140 husbands, 110 single
adult males, and 120 single adult females. It costs $2 to make a
daytime call and $4 (because of higher labor costs) to make an
evening call. The table shown below lists the expected results. For
example, 10% of all daytime calls are answered by a single male,
and 15% of all evening calls are answered by a single...
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