1. Consider the following hypothesis test:
H0: μ ≤ 50
Ha: μ > 50
A sample of 65 is used and the population standard deviation is 7. Use the critical
value approach to state your conclusion for each of the following sample results.
Use α = .05.
a. With x ¯ = 52.5, what is the value of the test statistic (to 2 decimals)?
Statistic = (52.5-50)/(7/√65) = 2.88 (rounded to 2 dp)
Answer: 2.88
Can it be concluded that the population mean is greater than 50?
YES OR NO?
Critical region ={ z/z>z(0.05)}={z/z>1.645}
Answer: yes, because the satstistic value is greater than 1.645
b. With x ¯ = 51, what is the value of the test statistic (to 2 decimals)?
Statistic = (51-50)/(7/√65) = 1.15 (rounded to 2 dp)
Answer: 1.15
Can it be concluded that the population mean is greater than 50?
YES OR NO?
Answer: No, because the statistic value is not greater than 1.645
c. With x ¯ = 51.8, what is the value of the test statistic (to 2 decimals)?
Statistic = (51.8-50)/(7/√65) = 2.07 (rounded to 2 dp)
Answer: 2.07
Can it be concluded that the population mean is greater than 50?
YES OR NO?
Answer: yes, because the satstistic value is greater than 1.645
2.Wall Street securities firms paid out record year-end bonuses of $125,500 per
employee for 2005 (Fortune, February 6, 2006). Suppose we would like to take a
sample of employees at the Jones & Ryan securities firm to see whether the mean
year-end bonus is different from the reported mean of $125,500 for the population.
a.State the null and alternative hypotheses you would use to test whether the yearend bonuses paid by Jones & Ryan were different from the population mean.
H0: μ Selectgreater than 125,500greater than or equal to 125,500equal to
125,500less than or equal to 125,500less than 125,500not equal to 125,500Item 1
Ha: μ Selectgreater than 125,500greater than or equal to 125,500equal to
125,500less than or equal to 125,500less than 125,500not equal to 125,500Item 2
b.Suppose a sample of 40 Jones & Ryan employees showed a sample mean yearend bonus of $118,000. Assume a population standard deviation of $30,000 and
compute the p-value (to 4 decimals).
Solution:
Statistic = (118,000-125,500)/(30,000/√40) = -1.581
p-value = 2P(z<-1.581) = 0.1139
Answer: p-value = 0.1139
c.With α = .05 as the level of significance, what is your conclusion?
SelectConclude that the year-end bonuses paid by Jones & Ryan were different
from the population meanDo not conclude that the year-end bonuses paid by Jones
& Ryan were different from the population meanItem 4
Answer the next three questions using the critical value approach.
d.Using α = .05, what is the critical value for the test statistic?
+/- z(0.025) = +/- 1.96
Answer: +/- 1.96
e.Calculate the test statistic (to 2 decimals).
See part b)
Answer: -1.581
f.Using α = .05, can you conclude that the year-end bonuses paid by Jones & Ryan were
different from the population mean?
YES OR NO?
Answer: NO
3. The U.S. Department of Labor reported the average hourly earnings for U.S.
production workers to be $14.32 per hour in 2001 (The World Almanac, 2003). A
sample of 75 production workers during 2003 showed a sample mean of $14.68 per
hour. Assuming the population standard deviation σ = $1.45, can we conclude that
an increase occurred in the mean hourly earnings since 2001? Use α = .05.
Ho: u ≤ 14.32
Ha: u > 14.32
Statistic = z = (14.68-14.32)/(1.45/√75) = 14.095
Critical value = z(0.05)= 1.645
Critical región = {z/z>1.645}
Decision: we reject Ho
Answer: Yes, we can conclude that an increase occurred in the mean hourly
earnings since 2001
4. The cost of a one-carat, VS2 clarity, H color diamond from Diamond Source
USA is $5600 (diasource.com, March 2003). A midwestern jeweler makes calls to
contacts in the diamond district of New York City to see whether the mean price of
diamonds there differs from $5600.
a. Formulate hypotheses that can be used to determine whether the mean price in
New York City differs from $5600.
H0: μ Selectgreater than or equal to 5600greater than 5600less than or equal to
5600less than 5600equal to 5600not equal to 5600Item 1
Ha: μ Selectgreater than or equal to 5600greater than 5600less than or equal to
5600less than 5600equal to 5600not equal to 5600Item 2
I need more info for the remaining parts
b. The p value is Selectless than .01between .01 and .02between .02 and .05between
.05 and .10between .10 and .20between .20 and .40greater than .40Item 3
c. Using α = .05, can you conclude that the mean price of the diamond is different in
New York?
SelectYesNoItem 4
Answer the next three questions using the critical value approach.
d. Using α = .05, what is the critical value for the test statistic? (+ or -)
e. State the rejection rule: Reject H0 if t is Selectgreater than or equal togreater
thanless than or equal toless thanequal tonot equal toItem 6 the lower critical value
or Selectgreater than or equal togreater thanless than or equal toless thanequal tonot
equal toItem 7 the upper critical value.
f. Using α = .05, can you conclude that the mean price of a diamond is different in
New York City?
YES OR NO