Normal Approximation to the Binomial and Poisson Distributions. Lognormal Distribution

1. In a classroom, 1 person in 6 students is left handed. If a class contains 40 students, what is the probability that 10 or more are left-handed? What is the probability that 10 or more are left-handed?

2. According to information available, an average of 3 accidents occurs every month in a certain junction of a city. But using suitable approximation, estimate the probability that at least 40 accidents occur at that busy junction in a year.

3. In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students, what is the probability that more than half are women?

4. In a company, the wages of a certain grade of staff are normally distributed with a standard deviation of RM400. If 20.05% of staff earn less than RM300 a week,

a. What is the average wage?

b. What percentage of staff earn more than RM500 a week?

Reading journal articles can be challenging for students, as they are often technical in nature. A high school that prides itself on preparing students for college wants to purchase journals that are written at a level accessible to students. The school librarian recruits four students with varying academic ability to read articles from four different journals and rate their readability from 1 (very difficult to read and understand) to 7 (very easy to read and understand). Some hypothetical data are shown in the table.

Table: Journal and Readability

a) Perform an F test at alpha level .05, using excel. Submit your workbook showing the results.

b) What is the conclusion in terms of the null hypothesis, reject or fail to reject? Explain why.

Data are provided to you on test completion times (in minutes) for students who participated in a one-hour review class before test number 1 and for these same students who were also administered test number 2 a month later. However, they did not participate in the review class before test number 2. The goal here is to determine whether there is a significant difference in the test completion time between the students when they had the review class compared to when they did not have the review class. Using software (or by hand):

A. Generate summary statistics (central tendency and variability measures) for the two samples and briefly summarize what they say.

B. Conduct a test of significance for the difference between the mean test completion times of students when they had the review class before the test and when they did not. Show and interpret the results.

C. Construct a 95% confidence interval of the difference between the two population mean test completion times and interpret it.

A survey was conducted to see if community college students preferred asynchronous distance learning (where learningoccurs through online channels without real-time interaction) or synchronous distance learning (where learning happens in real time, perhaps on Skype or Zoom).

Of the 250 students surveyed, 100 preferred asynchronous distance learning and 150 preferred synchronous distance learning. Construct a 95% confidence interval for the proportion of students who prefer asynchronous distance learning.

The local newspaper reported on the results of the survey by saying "over half of students prefer asynchronous distance learning". Is this statement supported by the confidence interval?

A) The 95% CI is (0.34,0.46). This interval does support the paper's statement.

B) The 95% CI is (0.34,0.46). This interval does not support the paper's statement.

C) The 95% CI is (0.54,0.66). This interval does not support the paper's statement.

D) The 95% CI is (0.54,0.66). This interval does support the paper's statement.

Next

Verbal SAT scores of incoming students at a large university were reported to have a mean of 580. At about the same time (2003), several hundred students in a variety of introductory statistics courses there were surveyed, and asked to report their Math and Verbal SAT scores.

1. Using the 391 students with nonmissing data for variable Verbal, test whether or not the sampled students' mean Verbal SAT score is consistent with a population mean of 580, reporting the P-value for a test of

H₀ : μ = 580 vs. H_a : μ ≠ 580. **Sample Mean =11.22

2.  Now carry out the same test, but assume population standard deviation to be 115, which is considerably larger than the sample standard deviation (73.24): report the P-value. (Round your answer to three decimal places.)

3. Assuming population standard deviation to be 115, set up a 95% confidence interval for population mean Verbal SAT score.

Consider two tests that could be used to evaluate a university’s effectiveness at teaching critical thinking and communication skills to undergraduates. The first test is a multiple-choice test with questions on reading comprehension, language, and math, similar to the SAT in the United States. The second test provides the students with a single real world case involving practical issues and data, including quantitative data, from several sources. The product that students produce for the second test is a memo, which must suggest a particular response to the case and support the decision with evidence and analysis. The second test is graded using specific criteria on critical thinking and communication (a rubric).

Discus the validity of each test for assessing the level of critical thinking and communication skills of students. Compare and contrast the two tests in terms of validity.

Discuss the reliability of each test for assessing the level of critical thinking and communication skills of students. Compare and contrast the two tests in terms of reliability.

1.Clearlystate the null and alternative hypotheses

2.Sketcha graph of the rejection region labeled with the criticalvalue(s)

3.Calculatethe test statistic (showing all workto earn any credit)and p-value(give a range of values for t, chi-square, and Fdistributions)

4.Write conclusion (3 sentences)

Five instructional and face-to-face delivery strategies were tested with students. Treatment group 1 had 10 students. Treatment group 2 had 15 students. Treatment group 3 had 10 students.Treatment group 4 had 17 students.Treatment group 5 had 13 students. Use the given table to conduct an ANOVA test to determine if the instructional delivery methods made a significant change in mean scores at α=.05.

1. Suppose the amount of money UCLA students spend on movies during a one month period observes normal distribution. A sample is taken containing monthly movie spending in dollars for several UCLA students as 66.72, 50.23, 40.57, 45.53, 60.45, 70.85, 57.49, and 53.46. Round your numbers to two decimal places. All the calculation should be preceded with the formula used.

a. Calculate the sample mean, sample standard deviation, and standard error.

b. Estimate the average monthly movie spending by all UCLA students with a 95% confidence interval.

c. From this sample, can we conclude that the average monthly movie spending by UCLA students is lower than 63.45 dollars at the 0.01 level of significance? (Show 7 steps)

d. Suppose the population standard deviation is known with a value of 7.14. Would the conclusions in b and c change? If yes, what would be the new conclusions? ? (Show 7 steps)