1.)The Mean Corporation would like to invest in the booming health food industry
ID: 3172359 • Letter: 1
Question
1.)The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $77,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $7,400.
The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit () earned by health-drink franchises. A random sample of 30 franchises were chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $78,950. The hypotheses that will be used by the statisticians are H0: = 77,000 and Ha: > 77,000.
a)Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places.
z =
b)Using the test statistic for the Mean Corporation's hypothesis test and level = 0.05, the Mean Corporation should accept/reject/not reject the null hypothesis.
c)If the sample size is increased to 60 (but the sample mean remains unchanged), the Mean Corporation should accept/reject/not reject the null hypothesis.
2.)
sample of 23 Menso members have had their Intelligence Quotients (IQs) measured and recorded. The data were used to calculate a 95% confidence interval for the mean IQ of all Menso members. The confidence interval was calculated as 148 ± 11. According to this confidence interval, it is most reasonable to conclude that:
a.)the mean IQ of all Menso members is between 137 and 159 b.)you are 95% confident the interval between 137 and 159 contains the mean IQ of all Menso members c.) 95% of all Menso members have an IQ between 137 and 159 d.)there is a 95% chance that the mean IQ of all Menso members is between 137 and 159Explanation / Answer
Q1.
Given that,
population mean(u)=77000
standard deviation, =7400
sample mean, x =78950
number (n)=30
null, Ho: =77000
alternate, H1: >77000
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 78950-77000/(7400/sqrt(30)
zo = 1.44332
| zo | = 1.44332
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.44332 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : right tail - ha : ( p > 1.44332 ) = 0.07446
hence value of p0.05 < 0.07446, here we do not reject Ho
ANSWERS
---------------
null, Ho: <77000
alternate, H1: >77000
test statistic: 1.44332
critical value: 1.645
decision: do not reject Ho
p-value: 0.07446
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