Suppose we somehow know that for the entire population of all students, the mean time spent exercising per week is 90 minutes, with a standard deviation of 40 minutes.

a) Would you expect time spent exercising per week to be normally distributed? Explain your reasoning. Consider your exercise habits as well as those of people you know.
b) We plan to collect random samples of 50 students and compute the sample mean time spent exercising, ?̅, for each sample. Would you expect the sampling distribution of ?̅, to be normally distributed? Explain briefly.
c) In approximately what proportion of samples would ?̅ be between 80 and 100 minutes?
d) Now suppose that the sample size is increased to 100 students per sample. In what proportion of
samples would ?̅ be between 80 and 100 minutes?

Q1 A researcher recorded the scores of 20 students in a written examination, trained in different methods, as shown below.

The data is arranged according to the training method used

TRAINING METHOD SCORES

Video Cassette 74 88 82 93 55 70

Audio Cassette 78 80 65 57 89

Classroom 68 83 50 91 84 77 94 81 92

1. Formulate and test the hypotheses to determine whether the examination scores among the 3 methods above are significantly different at 5% significance level

B Assume that you are carrying out a research at a university with 2000 students. How large a sample should you get to estimate the proportion of students who smoke to within a margin of error of ±5%, using any formulae. 10 marks

2) Using the excel data file “shopping” which shows the reasons American and East Asian students from a large Midwestern university may buy from catalogs.

a) (10 pts) For the Asian students make a pie chart of the reason they buy using a catalog. (Hint you will need to weigh cases by Asian)

b) (10 pts) Make a bar chart showing the counts for the reasons American students buy using a catalog. (Hint you will need to

weigh cases by American)

[Shopping Excel Data]

Suppose we somehow know that for the entire population of all students, the mean time spent exercising per week is 90 minutes, with a standard deviation of 40 minutes.

a) Would you expect time spent exercising per week to be normally distributed? Explain your reasoning. Consider your exercise habits as well as those of people you know.
b) We plan to collect random samples of 50 students and compute the sample mean time spent exercising, ?̅, for each sample. Would you expect the sampling distribution of ?̅, to be normally distributed? Explain briefly.
c) In approximately what proportion of samples would ?̅ be between 80 and 100 minutes?
d) Now suppose that the sample size is increased to 100 students per sample. In what proportion of
samples would ?̅ be between 80 and 100 minutes?

(1) Conditional Mean Table 1 is the probability of admission in the university. X=1 means that students are admitted; x=0 means that students are not admitted. Students are divided into two groups: male and Female.

Table 1: Admission Table

Admit . (x=1) Not Admit(x=0)

Male (0.3) . ( 0.2)

Female ( 0.4) . ( 0.1)

(a) Calculate the probability of admit, the probability of not admit, and the expectation of x.

(b)Calculate the probability of male, the probability of female, conditional probability of admit given male, conditional probability of not admit given male, conditional probability of admit given female, and conditional probability of not admit given female.

(c) Calculate the conditional expectation of x given male and the conditional expectation of x given female.

(d)Show that the expectation of x equals to the expectation of conditional expectation of x

1.) Use the given information below to find the confidence intervals. Show all work.

a.) Assuming conditions are met for inference, find the confidence interval for the population mean for the following information. The point estimate for the population mean is 8.9 and the standard error is 1.9569. The t value for a 95% confidence intervals is 2.0484. Round to the nearest tenths.

b.) A random sample of 60 part-time college students taking one math class spend an average of $200.00 for their textbook. A random sample of 40 part-time college students taking one sociology class spend an average of $180.00 for their textbook. The standard deviation in each case is $20.00. Find a 95% confidence interval for the difference in mean cost of textbooks for math and sociology students. Round to the nearest tenths.

A sample of size 30 students is to be drawn from a population consisting of 300 students belonging to two colleges A and B. the mean and standard deviations of their marks are given below:

1. How would you draw the sample using proportional allocation techniques? Hence, obtain the variance of the estimate of the population mean and compare its efficiency with simple random sampling without replacement (SRSWOR).
2. Variance of the estimate of the population mean for simple random sampling without replacement (SRSWOR).
3. Variance of the estimate of the population mean for proportional allocation
4. 95% confidence interval of the population mean for proportional allocation.

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

What are the null and alternative​ hypotheses?

Determine the test statistic. Round to two decimal places.

Determine the P-value. Round to three decimal places.

State the final conclusion that addresses the original claim.

______ H0. There is ______ evidence to conclude that the original claim that the mean of the population of estimated is 60 seconds _______ correct. It ________ that as a group the students are reasonably good at estimating one minute.

Questions 18 – 28. A researcher is interested in whether psychology students are less happy than other students. The mean happiness score for the population is 8. The researcher administers a happiness scale to 25 BC students and obtains a mean of 5 and variance of 49.The researcher uses an alpha level of 0.05.

18. Is this a one- or two-tailed test?

19. What is the null hypothesis?

20. What is the alternative hypothesis?

21. What are the degrees of freedom?

22. What is t critical?

23. What is the standard error?

24. What is the t statistic (t obtained)?

25. What decision would you make about H0?

26. What can you conclude?

27. What is the effect size?

28. What does this effect size mean?

A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes a random sample of 36 students who took a morning class and, independently, another random sample of 36 students who took an afternoon class. He finds that the morning group scored an average of 72 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ1 and µ2 represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. Compute the appropriate test statistic to analyze the claim at the 1% significance level.