BUS 219 / MAT 167 Summer, 2012 Final Exam 300 points
# Please show all pertinent steps. A top-notch solution is complete and is easy to # follow from beginning to end.
- The weights of first graders at Freemont Elementary were recorded as follows. Construct a frequency distribution (including cumulative frequency) using 6 classes and starting with 45.
45 50 60 65 62 57 62 65
49 46 50 51 58 62 67 71
- Find the range and variance of the following data set:
45, 51, 53, 76
- Find the mean and variance of the probability distribution:
- Compute the binomial probability if n = 21, p = 0.42, and x = 10
- A.C. Neilson reported that children between the ages of 4 and 9 watch an
average
of 22 hours of TV per week. Assume the variable is normally distributed and the standard deviation is 4 hours. find the probability that a randomly selected child will watch fewer than 18 hours of TV.
- The average teacher’s salary in Arizona is $42,300 with standard deviation $5000. Assuming a normal distribution, what is the probability that the mean of a sample of 50 teachers’ salaries will be at least $48,000 a year?
- If a baseball player's batting average is 0.275, find the probability that the player will get at least 40 hits in 100 times at bat.
Thirty
randomly selected vehicles were stopped, and the tread depth of the right front tire was measured. The mean was 0.20 inch, and the standard deviation was 0.05 inch. Find the
95%
confidence interval of the mean depth. Assume the variable is approximately normally distributed.
- A statistics instructor is asked to estimate the average age of students at the college at
99%
confidence with accuracy within 2 years. A previous study determined that the standard deviation was 5 years. How large a sample is needed?
- Ten randomly selected cars were stopped and the tread depth of the left
front tire measured. The mean was 0.12 inch, and the standard deviation
was 0.02 inch. Find the
90%confidence interval of the mean depth.
- In a recent study of 250 female freshmen showed that 70 did not want to work after marriage. Find the
95%
confidence interval of the true proportion.
- Find the
99%
confidence interval for the variance and standard deviation for the lifetime of batteries if a sample of 40 has a standard deviation of 3.4 months. Assume the variable is normally distributed.
- A researcher wishes to test the claim that the average age of lifeguards is greater than 22 years. The researcher sampled 56 lifeguards and found an average of 23.7 years with a standard deviation of 2 years. Test the claim at “alpha” =
0.05.
- A researcher reports that the
average
salary of assistant professors is more than $67,000. A sample of 18 such professors has a mean salary of $71,000. At "alpha" =
0.05, test the claim that assistant professors earn more than $67,000 per year. The standard deviation of the population is $5500.
- A telephone company estimates that
55%
of its customers have call-waiting service. To test this hypothesis, 110 customers are sampled and 48% have call-waiting. At “alpha” =
0.01, is there enough evidence to reject the claim?
- A researcher knows from past studies that the
standard deviation
of times it takes to inspect a car is 17.3 minutes. A sample of 27 cars is selected and inspected. The standard deviation was 7.5 minutes. At “alpha” =
0.01, can it be concluded that the standard deviation is not 17.3 minutes?
- A survey found that the
average
hotel room rate in New Orleans is $89 and the average room rate in Phoenix is $77. Assume that the data were obtained from two samples of 95 each and that the standard deviations were $14 and $9 respectively. At "alpha" =
0.05, can it be concluded that there is no significant difference in the rates?
- A medical researcher wishes to see whether the
variances
of the heart rates (in beats per minute) of smokers are different from the variances of heart rates of people who do not smoke. Two samples are selected, and the data is as below. Using "alpha" =
0.10, is there enough evidence to support the claim?
Smokers Nonsmokers
- A study was conducted to determine if the percent of women who receive financial aid was different than the percentage for men. At "alpha" =
0.10, is there significant evidence to reject the null hypothesis?
Women MenSample size 270 325
Number receiving aid 190 210
- A manager wants to know whether there is a relationship between the number of radio ads per week and the amount of sales ($ in thousands). The data collected are:
- Draw the scatter plot for the variables.
- Test the significance of the correlation coefficient at “alpha” =
0.05.
- Write the regression equation and include it on the scatterplot.
- A bank manager wishes to see whether there is any
preference
in the times that customers use the bank. Six hours are selected, and the number of customers visiting the bank are as shown here. At "alpha" = 0.01, do the customers show a preference for specific times?
TIME 10:00 11:00 NOON 1:00 2:00 3:00
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# CUSTOMERS 20 35 42 34 30 19
- A convenience store owner hypothesizes that the
median number
of snow cones he sells per day is 36. A random sample of
20
days yields the following data for the number of cones sold each day. At "alpha" =
0.05, test the owner's hypothesis.
18 43 10 16 22 30 29 32 37 36
39 34 39 30 28 30 40 34 39 52
- A researcher wishes to try three different techniques to lower blood pressure. Subjects are randomly assigned to three groups, as indicated in the table below. After four weeks, the reduction in each person’s blood pressure is recorded. At “alpha” =
0.05, test the claim that there is
no difference among the means. In the event that the null hypothesis is rejected, do not perform a follow-up test (Tukey or Scheffe)
Medication Exercise Diet 8 9 15
11 10 10
10 11 12
12 13 11
14 12 9
- To test the claim that there is no difference in the lifetimes (in months) of two brands of video games, a sample of each was selected as indicated in the table. At “alpha” =
0.01, can we conclude that there is a difference?
Brand A42 34 39 42 22 47 51 34 41 39 28
Brand B29 39 38 43 45 49 53 38 44 43 32
- 28 29 32 34 34 38 38 39 39 39 41 42 42 43 43 44 45 47 49 51 53
1 2 3 4 5.5 7.5 10 10 10 12 13.5 15.5 17 18 19 20 21 22
A A B B A A B B A B A A A A B B B B A B A B