Problem 5

a) Suppose that, in a random sample of 40 accounting students who had their second co-op term in W19, the sample mean and hourly wage and standard deviation were $20.10 and $3.15, respectively. Calculate a 95% confidence interval for the mean hourly wage of all accounting students with a second co-op term in W16. Interpret your interval.

b) Suppose that based on historic data accounting students on their first co-op term typically earn an average of $17.84 per hour. Does the data collected in part a) suggest that accounting students in their second co-op earn on average more than those on their first co-op? Perform a hypothesis test at a 10% level of significance to test this. Clearly state your conclusion.

The population of all Harvard students spends an average of $330 per semester on books. The population standard deviation of this expenditure is $65. A simple random sample of 40 students who attend the college is taken.

a. Provide the sampling distribution for the sample mean. Can you assume a normal distribution for the sample mean? Why or why not?

b. Calculate the probability that the average expenditure for the 40 students in the sample is between $320 and $350.

c. Calculate the probability that the average expenditure for the 40 students in the sample is less than $300.

d. If we increase the sample size to 50, show and explain what happens to the standard error. Without showing calculations, how would this change in sample size affect the probabilities you calculated in both b and c? Be specific.

A survey is given to 300 random SCSU students to determine their opinion of being a “Tobacco Free Campus.” Of the 300 students surveyed, 228 were in favor a tobacco free campus.

1. Find a 95% confidence interval for the proportion of all SCSU students in favor of a tobacco free campus.
2. Interpret the interval in part a.
3. Find the error bound of the interval in part a.
4. The Dean claims that at least 70% of all students are in favor of a tobacco free campus. Can you support the Dean’s claim at the 95% confidence level? Justify!

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject Ho, and your conclusion in the words of the claim. For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=542.7 and standard deviation σ=29.8.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 546 or higher?
ANSWER:  

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯, of 35 students?
The mean of the sampling distribution for x¯is:  
The standard deviation of the sampling distribution for x¯ is:

(c) What z-score corresponds to the mean score x¯ of 546?
ANSWER:

(d) What is the probability that the mean score x¯ of these students is 546 or higher?
ANSWER:  

A recent national survey found that high school students watched an average of 6.8 DVDs per month with a population standard deviation of 0.5 DVDs. The distribution follows the normal distribution. A random sample of 36 college students revealed that the mean number of DVDs watch last month was 6.2. At the .05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?

a. What is the null and alternative hypotheses?

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

c. Which distribution should we use? Normal or Student t

d. What is the critical value(s)? (the line in the sand values)

e. What is your test statistic value?

f. What is the p-value

g. What is your decision regarding the null hypothesis?

According to the 2016 CCSSE data from about 430,000 community college   students nationwide, about 13.5% of students reported that they “often” or “very often” come to class without completing readings or assignments.

Are the results similar at community colleges in California? Specifically, let’s test the claim that California students are different. Use a 5% level of significance.

Suppose that the CCSSE is given in California to a random sample of 500 students and 10.5% report that they “often” or “very often” come to class without completing readings or assignments.

a) State the hypotheses in words and write a sentence to explain what p represents.

b)Verify that the normal model is a good fit for the distribution of sample proportions.

c) Test the claim by a significance test( 6-steps, show all calculations)

d)State your conclusion.

study of the effect of college student employment on academic performance, the following summary statistics for GPA were reported for a sample of students who worked and for a sample of students who did not work. The samples were selected at random from working and nonworking students at a university. (Use a statistical computer package to calculate the P-value. Use μ_employed − μ_{not employed}. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t= df= P=
Does this information support the hypothesis that for students at this university, those who are not employed have a higher mean GPA than those who are employed? Use a significance level of 0.05.

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=548.8μ=548.8 and standard deviation σ=26.4σ=26.4.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 555 or higher?
ANSWER:

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯x¯, of 35 students?
The mean of the sampling distribution for x¯ is:
The standard deviation of the sampling distribution for x¯ is:

(c) What z-score corresponds to the mean score x¯ of 555?
ANSWER:

(d) What is the probability that the mean score x¯ of these students is 555 or higher?
ANSWER:

Problem#5: The Birthday Problem (10pts) In your classroom there are 45 students, assume that none of them is born on February 29, and hence consider only common years (365 days) [do not consider leap years]. 1- Take a student randomly from the class, what is the probability that he have the same birthday as yours? 2- What is the probability that there is at least one student in the class having the same birthday as yours? 3-What is the probability that there is no repeated birthday date in the class (all the 45 birthdays being different)? Comment on the value you found 4- The instructor decides to nominate 5 students randomly to deliver a presentation next class, • How many groups (of five students) are possible? • What is the probability that you are among the selected students?

Consider an automated plagiarism detection software that is used to evaluate essay submissions. Four sections of a writing course use the software to check for plagarism, with 30% of the students in section 1, 16% in section 2, 30% in section 3, and 24% in section 4. In section 1 of a course, 20% of the essays are flagged, in section 2, 23%, section 3, 15% and section 4, 8%. (a) What percentage of total students committed plagiarism overall? (b) Given that a particular student committed plagiarism, what in the probability that they were registered for section 1 of the course. (c) Given that a particular student committed plagiarism, what in the probability that they were registered for section 2 of the course. (d) If there are 200 students registered between these 4 sections, how many students in section 3 cheated?