Test the claim that the mean GPA of Orange Coast students is significantly different than the mean GPA of Coastline students at the 0.2 significance level.

The null and alternative hypothesis would be:

H0:pO≥pCH0:pO≥pC
H1:pO<pCH1:pO<pC

H0:μO=μCH0:μO=μC
H1:μO≠μCH1:μO≠μC

H0:μO≥μCH0:μO≥μC
H1:μO<μCH1:μO<μC

H0:μO≤μCH0:μO≤μC
H1:μO>μCH1:μO>μC

H0:pO=pCH0:pO=pC
H1:pO≠pCH1:pO≠pC

H0:pO≤pCH0:pO≤pC
H1:pO>pCH1:pO>pC

The test is:

left-tailed

right-tailed

two-tailed

The sample consisted of 20 Orange Coast students, with a sample mean GPA of 2.06 and a standard deviation of 0.02, and 20 Coastline students, with a sample mean GPA of 2.03 and a standard deviation of 0.08.

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

The town hall of a city wants to open some recreational centers. It has been analyzed 3 options. The opening cost and the capacity of each center are listed below.

The selected recreational centers must be hosting the students from 5 schools. In the table below is summarized the number of students at each school.

Each school must be assigned to only one recreational center. And the capacity of each center must be respected. What are the recreational centers that must be open in order to minimize the opening cost?

Illustrate the greedy procedure with the following data:

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 1111 nursing students from Group 1 resulted in a mean score of 56.356.3 with a standard deviation of 6.16.1. A random sample of 66 nursing students from Group 2 resulted in a mean score of 64.164.1 with a standard deviation of 6.56.5. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1μ1 represent the mean score for Group 1 and μ2μ2 represent the mean score for Group 2. Use a significance level of α=0.01α=0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 3 of 4:

Determine the decision rule for rejecting the null hypothesis H0H0. Round your answer to three decimal places.

a) The 10 members of the committee have to choose one president and two vice presidents (these have to be three different people). In how many ways can they choose these officers? (Note: here is no distinction between the two vice presidents; there is not a “first” VP and a “second” VP).

b) Three couples go to a movie theater. They sit in consecutive seats such that each couple is seating together, that is each person is seating next to his/her partner. If there are 6 seats available, in how many ways can they sit?

c) A university wants to assign a three digit number to each classroom of a new building. They can use the digits {1,2,3,4,5} but they cannot use any digit more than once. How many classroom numbers can they assign if the numbers have to be less than 250?

d) The University wants to select 4 students for a feedback survey. They want all four students from either Prof. X’s section or Prof. Y’s section. Prof. X has 40 students in his class and Prof. Y has 30 students in his class. How many selections are possible?

A professor decides to conduct a experiment to determine the effects of using a study sheet on final performance among her students. She is interested in finding out if creating a study sheet improves performance on the final. Prior to the start of the semester, the professor randomly assigns 16 students to one of two groups. One group of students is given a direction to create a study sheet over the course of the term and the other group is not. Both groups receive the same course content over the course of the semester. Scores from the final are used as the dependent variable. Below are the scores for the final of students in her class.

Study Sheet: 88, 77, 96. 85, 71, 73, 81, 91
No study sheet: 63, 71, 83, 90, 92, 84, 72, 71

a.  Is this an independent samples or related samples design? Why?
b.  Write the H0 and H1 in symbols.
c,  Calculate the degrees of freedom (df) and the t critical value with a significance level of .05.
d.  Use the data and conduct the appropriate test to test the hypothesis that creating a study sheet will improve performance on the final
e. Report your decision.
f. Interpret your finding.

A psychology professor decides to conduct a scientific experiment to determine the effects of using a study sheet on test performance among her students. She is interested in finding out if creating a study sheet improves performance on the test. Prior to the start of the semester, the professor randomly assigns 16 students to one of two groups. One group of students is given a direction to create a study sheet over the course of the term and the other group is not. Both groups receive the same course content over the course of the semester. Scores from the test are used as the dependent variable. Below are the scores for the test of students in her class.

Study Sheet: 88, 77, 96. 85, 71, 73, 81, 91

No study sheet: 63, 71, 83, 90, 92, 84, 72, 71

a. Is this an independent samples or related samples design? Why?

b. Write the H0 and H1 in symbols.

c, Calculate the degrees of freedom (df) and the t critical value with a significance level of .05.

d. Use the data and conduct the appropriate test to test the hypothesis that creating a study sheet will improve performance on the test.

e. Report your decision.

f. Interpret your finding.

You want to find out the percentage of community college students that own a pet. You decide to email five students in one of your classes and ask them if they own any pets.

(a) What is the population in this example?

(b) What is the sample?

(c) What is the parameter of interest?

(d) Suppose three of the five students tell you they own a pet, while the other two say they do not. i. Is this numerical or categorical data?

Explain your answer. ii. What is the value of the statistic of interest in this survey? Show a calculation.

(e) Have you taken a simple random sample of the population? Explain your answer. (f) Do you think this sample will be representative? Explain your reasoning.

2. You later do a larger survey of 20 community college students. You ask each of the 20 people the question “How many pets do you own?”

Here is the data you collected. 5,2,4,1,0,0,1,3,2,7,6,0,0,1,1,3,2,2,1,5. Make a table that shows the frequency, relative frequency, and cumulative relative frequency of the responses.

3. Draw a histogram of the data from the previous problem, using four class intervals, i.e., using four bars.

Test the claim that the mean GPA of Orange Coast students is significantly different than the mean GPA of Coastline students at the 0.2 significance level.

The null and alternative hypothesis would be:

H0:pO=pCH0:pO=pC
H1:pO≠pCH1:pO≠pC

H0:μO≥μCH0:μO≥μC
H1:μO<μCH1:μO<μC

H0:μO≤μCH0:μO≤μC
H1:μO>μCH1:μO>μC

H0:μO=μCH0:μO=μC
H1:μO≠μCH1:μO≠μC

H0:pO≤pCH0:pO≤pC
H1:pO>pCH1:pO>pC

H0:pO≥pCH0:pO≥pC
H1:pO<pCH1:pO<pC

The test is:

left-tailed

two-tailed

right-tailed

The sample consisted of 20 Orange Coast students, with a sample mean GPA of 2.79 and a standard deviation of 0.07, and 20 Coastline students, with a sample mean GPA of 2.81 and a standard deviation of 0.05.

The test statistic is: (to 2 decimals)

The p-value is: (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

3. The population of male students at Gallup (NM) Community College have a men height of 67.5 inches. It is claimed that male students who try out for the basketball team are taller than the general population of male students. To test this claim a sample of n= 36 male students who try out for the basketball team have a mean height of 68.3 inches and a standard deviation of 2.8 inches. Test this claim at the 90 and 99% levels.

a) State the null hypothesis________________________

b) State the alternative hypothesis ________________________

c) In this problem, is it a one or two tail test? ________________

At the 90% confidence level, d) what is the critical value(s)?__________
e)What is the critical region to fail to reject null hypothesis?___________

f. What is the critical region to reject the null hypothesis? ____________

g) Compute the test statistic (show work)

h) What is the decision (at the 90% level) _________________.

at the 99% confidence level, i) what is the critical value(s)? ____________.

j) What is the critical region to fail to reject the null hypothesis?___________ .

k) What is the critical region to reject the null hypothesis? ____________.

You already did the test in part g)

L) What is the decision (at the 99% confidence level) _____________.

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 90

words per minute​ (wpm) and a standard deviation of 10 wpm. Complete parts​ (a) through​ (e).

(a) What is the probability a randomly selected student in the city will read more than 94 words per minute? (Round to four decimal places as needed.)

(b) What is the probability that a random sample of 12 second grade students from the city results in a mean reading rate of more than 94 words per minute? (Round to four decimal places as needed.)

(c) What is the probability that a random sample of 24 second grade students from the city results in a mean reading rate of more than 94 words per​ minute? (Round to four decimal places as needed.)

(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result.

(e) A teacher instituted a new reading program at school. After 10 weeks in the​ program, it was found that the mean reading speed of a random sample of 19 second grade students was 92.3 wpm. What might you conclude based on this​ result?