In a particular country, it is known that college students report falling in love an average of 2.20 times during their college years. A sample of five college students originally from that country but who have spent their entire college career in Canada, were asked how many times they had fallen in love during their college years. Their numbers were 2, 3, 5, 5, and 2.

Using the .05 significance level, do exchange students like these who go to college in Canada fall in love more often than those who complete their studies in their country of origin?

Use the hypothesis–testing steps to answer this.

ONE SAMPLE T TEST

A random sample of 22 students’ weights from the student population of palamar college were taken. The average weight of the population of college students is µ = 140. The 22 students in the sample had the following weights:

X

135   205
119   195
106   185
135   182
180   150
108   175
128   190
160   180
143   195
175   220
170   235

Please state your null hypothesis and alternative hypothesis, both as an equation and in your own words. After you run the data through SPSS, please write up the results.

1) A statistics professor is examining if using the book in his class has any impact on student test scores. For a sample of 30 Statistics students who were required to buy and read the book for class, final semester grades were measured at the end of the semester. The mean final grade for this class was 87. If the mean final grade for all the previous classes (where students had not been required to use the book) was 83 with a standard deviation of 5, can the professor conclude that using the textbook changes students’ grades significantly? (Set the alpha level at .05)

a. Complete all steps of the hypothesis test to test the null hypothesis.

Suppose a MTH instructor is teaching two sections of the course, and administers an exam. The instructor grades the exams, and calculates the mean exam score to be 65 for section 1 and 83 for section 2.

a- Do you (not the instructor) have enough information to calculate the overall mean for all students enrolled on either section? Explain

b- Suppose section 1 has 35 students and section 2 has 25 students. Calculate the overall mean. Is the overall mean closer to 65 or to 83?

c- Give an example of two section sizes n1 and n2 for which the overall mean is more than 81 (show your calculation)

A random sample of 19 rainbow trout caught at Brainard lake, Colorado, had mean length x = 11.9 inches with sample standard deviation o 2.8 inches.
Find a 95% confidence interval for the population mean length of all rainbow trout in this lake.
b. interpret the meaning of the confidence interval in the context of this problem .

A random sample of 78 students was interviewed, and 59 students said that they would vote for Jennifer James as student body president.
a. Let p represent the proportion of all students at this college who will vote for Jennifer. Find a point estimate p for p.
b. Find a 98% confidence interval for p.

Assume that the average amount of money spent on video games is normally distributed with a population standard deviation of 12.42 AED. Your friend wants to estimate the expenditure on video games, takes a sample of 10 students, and finds that the mean expenditure is 50.77 AED. a. Estimate with 99% confidence the average amount of expenditure on video games. b. How many students you need to sample in order to be within 5 AED, with 95% confidence? c. Assume that your friend told you that the average amount of expenditure from these 10 students should be at least 75 AED. Do you think he is correct? Explain using probabilities.

4) Educators introduce a new math curriculum and measure 45 students' scores before and at the end of the academic year using an exam widely believed to accurately measure students' understanding. The average score at the start the year was 65%, and after was 75%.

a) In words, what are the null and alternative hypothesis tests that the educators would most likely be interested in testing?
b) What does a hypothesis test tell us that we can't learn from simply noting that students improved 10 percentage points?
c) Suppose the p-value from this hypothesis test was 0.54. Explain how to interpret this value in this context.

1. The Scholastic Aptitude Test (SAT) contains three areas: critical reading, mathematics, and writing. Each area is scored on an 800-point scale. A sample of SAT scores for six students follows.
   1. Using a .05 level of significance, do students perform differently on the three areas of the SAT?
   2. Which area of the test seems to give the students the most trouble? Explain.

Every semester, I would like for more than 75% of my students to score a 70 or higher on the first test. This semester, out of the 72 students who took the first test, 59 got at least a C (scored higher a 70 or higher). Is there sufficient evidence to conclude, at the 10% significance level, that more than 75% of the students got at least a C on the first exam? Find the p-value.

Identify the null and alternative hypotheses, test statistic, critical value(s) and critical region or p-value, as indicated, and state the final conclusion that addresses the problem. Show all seven steps.

Do College students who have volunteered for community service work differ from those who have not? A study obtained data from 57 students who had done service work and 17 who had not. One of the response variables was a measure of attachment to friends, measured by the Inventory of Parent and Peer Attachment. Here are the results. Group Condition n x s__ 1 Service 57 105.32 14.68 2 No Service 17 96.82 14.26 a. Do these data give evidence that students who have engaged in community service and those who have not differ on average in their level of attachment to their friends?