business stats 10 questions in attached file.?please show all work.?
1. The manager of a local store believes that the store?s average daily sales are more than $8,000. To
test her belief, a sample of 64 days of sales was selected; and it was found that the average daily
sale was $8,250 with a standard deviation (of the sample ) of $1,200.
a. Perform a hypothesis test of the manager?s belief at the 5% level of significance.
b. What is the p-value of this test and state its meaning. 2. From a population of cereal boxes marked ?12 ounces?, a sample of 16 boxes is selected and the
contents of each box is weighed. The sample revealed a mean of 11.7 ounces with a standard
deviation of 0.8. Test to see if the mean of the population is at least 12 ounces. Use a .05 level of
significance. 1. The business manager of a local health clinic is interested in estimating the difference between
the fees for extended office visits in their center and the fees of a newly opened group practice.
He gathered the following information regarding the two offices:
Health Clinic Group Practice n1 = 50 visits
= 21 n2 = 45 visits
= 19 S1 = 2.75 S2 = 3.00 x x Test to see if there is a significant difference between the fees charged by the two clinics. Use
a 5% level.
4. A large corporation wants to determine whether or not the ?typing efficiency? course given at
the local college has any influence on the typing speed of their secretaries. A sample of 6
secretaries is selected, and they are sent to take the course. The typing speed of the secretaries in
words per minute ( WPM ) are shown below: Sec?y
6 WPM Before
65 WPM After
67 Use a 5% level and test to see if we can conclude that taking the course will actually increase
the average typing speed of the secretaries.
5. The producer of Viagrow, a plant fertilizer, claims that their bagging equipment is very accurate
and that the standard deviation of all their filled bags is 0.1 ounce or less. A sample of 20 bags
showed a standard deviation of 0.11. Does this sample result confirm the claim of the
manufacturer? Use a 5% level. 6. The salaries of managers at 423 convenience stores is believed to be normally distributed. A
random sample of eighteen managers is chosen. The sample average salary is $31,520 with a
standard deviation of $1,560. Find the 95% confidence interval for the average salary of
managers at the 423 convenience stores. 7. Eighteen out of twenty managers at a large discount auto chain have college degrees. Determine
the probability that a random sample of 4 managers contains:
a. Three managers who have college degrees
b. At least three managers who have college degrees
c. No manager has a college degree. 8. A statistics professor wishes to find out the relationship between the classification of a student
and the students? grade in the course. The following is a breakdown of the grades and
classification of students in three sections of the course. (Hint: Transform the raw data below
into marginal and joint probabilities) Grade
F First Year
a. The probability that a randomly selected student makes a D or F in the course.
b. The probability that a randomly selected student is a junior and makes at least a B in the
c. Given that we have randomly selected a senior, what is the probability that they will not
make an A in the course?
9. A local super market has installed a self-service checkout counter. If X is the number of
customers who check out through self-service during a 10 minute period and we assume that the
conditions of the Poisson random variable are satisfied with a mean of 6 customers per 10 minute
period, what is the probability that:
a. Exactly 6 customers will check out during any 10 minute period?
b. No more than 5 customers will check out during any 10 minute period?
c. Exactly 4 customers will check out during any 15 minute period? 10. The following data represent the number of weed-eaters sold per month at the local garden shop
and their prices: (Use the readout below to answer the questions) Price
40 Units sold
1 a. Develop a least squares estimated regression line. Identify the meaning of the slope and
intercept of this estimated line.
b. Could we use this estimate to predict the number of units sold if the price was 25?
c. What hypothesis test is being performed here?
d. What is the meaning of the R2 here? How was this derived? SUMMARY OUTPUT
Adjusted R Square
29.62415 t Stat
0.002842 Significance F
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