An educator has the opinion that the grades high school students make depend on the amount of time they spend listening to music. To test this theory, he has randomly given 400 students a questionnaire. Within the questionnaire are the two questions: “How many hours per week do you listen to music?” “What is the average grade for all your classes?” The data from the survey are in the following table. Using a 5 percent signifi cance level, test whether grades and time spent listening to music are independent or dependent.
At the 0.10 level of signifi cance, can we conclude that the following 400 observations follow a Poisson distribution with λ = 3?
After years of working at a weighing station for trucks, Jeff Simpson feels that the weight per truck (in thousands of pounds) follows a normal distribution with μ = 71 and σ = 15. In order to test this assumption, Jeff collected the following data one Monday, recording the weight of each truck that entered his station.
Below is an observed frequency distribution. Using a normal distribution with μ = 5 and σ = 1.5,
- Find the probability of falling in each class.
- From part (a), compute the expected frequency of each category.
- Calculate the chi-square statistic.
- At the 0.10 level of signifi cance, does this frequency distribution seem to be well described by the suggested normal distribution?
At the 0.05 level of signifi cance, can we conclude the following data follow a Poisson distribution with λ = 5?
Louis Armstrong, salesman for the Dillard Paper Company, has five accounts to visit per day. It is suggested that the variable, sales by Mr. Armstrong, may be described by the binomial distribution, with the probability of selling each account being 0.4. Given the following frequency distribution of Armstrong’s number of sales per day, can we conclude that the data do in fact follow the suggested distribution? Use the 0.05 significance level.
The computer coordinator for the business school believes the amount of time a graduate student spends reading and writing e-mail each weekday is normally distributed with mean μ = 14 and standard deviation σ = 5. In order to examine this belief, the coordinator collected data one Wednesday, recording the amount of time in minutes each graduate student spent checking e-mail. Using a chi-square goodness-of-fi t test on these data, what would you conclude about the distribution of e-mail times? (Use a 0.05 significance level and clearly state your hypotheses.) (Hint: Use five equally probable intervals.)
In order to plan how much cash to keep on hand in the vault, a bank is interested in seeing whether the average deposit of a customer is normally distributed. A newly hired employee hoping for a raise has collected the following information:
The post offi ce is interested in modeling the mangled-letter problem. It has been suggested that any letter sent to a certain area has a 0.15 chance of being mangled. Because the post offi ce is so big, it can be assumed that two letters’ chances of being mangled are independent. A sample of 310 people was selected and two test letters were mailed to each of them. The number of people receiving zero, one, or two mangled letters was 260, 40, and 10, respectively. At the 0.10 level of signifi cance, is it reasonable to conclude that the number of mangled letters received by people follows a binomial distribution with p = 0.15?
A state lottery commission claims that for a new lottery game, there is a 10 percent chance of getting a $1 prize, a 5 percent chance of $100, and an 85 percent chance of getting nothing. To test whether this claim is correct, a winner from the last lottery went out and bought 1,000 tickets for the new lottery. He had 87 one-dollar prizes, 48 hundred-dollar prizes, and 865 worthless tickets. At the 0.05 signifi cance level, is the state’s claim reasonable?