A high school teacher is interested to compare the average time for students to complete a standardized test for three different classes of students.       

The teacher collects random data for time to complete the standardized test (in minutes) for students in three different classes and the dataset is provided below.    

The teacher is interested to know if the average time to complete the standardized test is statistically the same for three classes of students. Use a significance level of 5%.

The teacher has confirmed that the samples were randomly selected and independent, and the populations have normal distribution and the population variances are equal.

(a) calculate the Test Statistic for this example (round your answer to 2 decimal places)

(b) calculate the P-value for this example (round your answer to 2 decimal places)

The Ministry of Education wants to know whether attending a private school has a positive causal effect on student test scores. The Ministry provides you with data that covers all students in the province of Ontario. The data include each student's grade average and whether he or she attends a public or private school. Note that attending a private school is an active choice made by students and parents (all students are guaranteed a spot in a public school) and students are required to pay tuition to attend (public schools are free).

You define the independent variable of interest as

??=   1 if student attends a private school

  0 otherwise

Let ??? denote the grade average of student ?. You consider estimating the following regression in order to evaluate the effect of attending a private school on student grade average:

???=?0+?1??+??

Please answer the following questions.

a/ Interpret the parameter ?0. What does it represent?

b/ Interpret the parameter ?1. What does it represent?

c/Using the econometric model given by the equation above (???=?0+?1??+??), write down (mathematically) the condition that must be satisfied for OLS estimation of this model to result in an unbiased estimate of ?1. Now interpret this condition (in words). Do you think the condition is satisfied?

d/ Would your answer to question (1c) above change if heteroskedasticity was present in this model? If so, explain how. If not, why not? Make sure to (briefly) define heteroskedasticity in your answer.

1- Students had a mean grade of 70% in the past. After applying a new teaching method, the following scores were recorded for a sample of 9 random students:

In order to construct a 95% confidence interval for the new mean grade, we should use:

• 1-PropZInt
• ZInterval
• 2-SampZInt
• 2-SampTInt
• TInterval
• 2-PropZInt

2-

Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 336 with 81 successes. Enter your answer using decimals (not percents) accurate to three decimal places.

< p <

3-

A test was given to a group of students. The grades and gender are summarized below:

Let pp represent the percentage of all female students who would receive a grade of A on this test. Use a 80% confidence interval to estimate pp to three decimal places.

Enter your answer using decimals (not percents).

<p <

4-

Out of 500 people sampled, 295 preferred Candidate A.

Based on this, find a 90% confidence level for the true proportion of the voting population (pp) prefers Candidate A.

Give your answers as decimals, to three places.

<p<

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 10 nursing students from Group 1 resulted in a mean score of 55.9 with a standard deviation of 5.4. A random sample of 14 nursing students from Group 2 resulted in a mean score of 64.5 with a standard deviation of 5.7. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed. Step 2 of 4 : Compute the value of the t test statistic. Round your answer to three decimal places. Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places. Step 4 of 4: State the test's conclusion. A. Reject Null Hypothesis B. Fail to Reject Null Hypothesis

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 15 nursing students from Group 1 resulted in a mean score of 59.659.6 with a standard deviation of 8.1. A random sample of 12 nursing students from Group 2 resulted in a mean score of 65.5with a standard deviation of 5.2. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to two decimal places.

Step 4 of 4: Make the decision for the hypothesis test.

The p-value was slightly above conventional threshold, but was described as “rapidly approaching significance” (i.e., p =.06). An independent samples t test was used to determine whether student satisfaction levels in a quantitative reasoning course differed between the traditional classroom and on-line environments. The samples consisted of students in four face-to-face classes at a traditional state university (n = 65) and four online classes offered at the same university (n = 69). Students reported their level of satisfaction on a fivepoint scale, with higher values indicating higher levels of satisfaction. Since the study was exploratory in nature, levels of significance were relaxed to the .10 level. The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the online sections (M = 3.89, SD = 1.4). We therefore conclude that on average, students in online quantitative reasoning classes have higher levels of satisfaction. The results of this study are significant because they provide educators with evidence of what medium works better in producing quantitatively knowledgeable practitioners.

How do I evaluate the sample size?

How do I evaluate the statements for meaningfulness?

How do I evaluate the statistical significance?

How do I provide an explanation of the implications for social change?

1. Statistics at a certain college has been historically taught at two times: at 8 am and at 4 pm.

A random sample of 150 students that took the morning class results in a mean score of 81.2 points, with a standard deviation of 18 points, and a random sample of 150 students that took the afternoon class results in a mean score of 76.4 points and a standard deviation of 21 points. For this problem, assume that the sample sizes are large enough so that the sample standard deviations (S) are good approximations for the unknown population standard deviations (σ).

a. Compute a 95% confidence interval for the mean score for all students taking statistics at 8 am.

b. Compute a 95% confidence interval for the mean score for all students taking statistics at 4 pm.

c. Based on the confidence intervals, is there strong evidence to support the claim that the morning classes do better in statistics? Explain.

2. A poorly written research paper states a confidence interval for the mean reaction time to an experiment as 83.6 ± 11.515 seconds, but forgot to mention what the confidence level was. However, the paper did say that the population standard deviation is σ = 35, and the sample size was n = 25.

a. What was the confidence level used for the confidence interval stated in the paper? b. Using the same sample results, how could you lower the margin of error to below 10 seconds?

Suppose that during an unexpected snowstorm, Mr. Wong decided to take a random sample of students in his AP Statistics class to examine their arrival times, in minutes. He compared the difference between the students' arrival time with the time the class was supposed to begin.

Mr. Wong asks you, his assistant, to use the information below to answer the following questions (negative value means that the student arrived BEFORE class began).

* Please do not copy other experts' solutions, thank you!

Question A: Mr. Wong would like to determine if his students arrive to class late on average. He asks you to perform a hypothesis test @ 10% significance level. Clearly state the conclusion you would tell Mr. Wong using a critical value.

Question B:

i) Mr. Wong asks you to calculate a 90% confidence interval for the average difference in time.

ii) Interpret the interval you calculated.

iii) Based on the interval, what can you say about Mr. Wong's AP Statistics class's arrival time?

Question C: Did you expect the conclusion in Question B to be the same as the conclusion in Question A? Explain why or why not.

1. A school administrator sends out grade school students to sell boxes of candy to raise funds. Below is a selection of four students and the mean number of boxes they sold over a weekend. The administrator wants to calculate the average number of boxes sold across students, but wants to weight this by the number of nearby houses (because students with more houses nearby will sell more boxes). For these data, what is the weighted mean?

2.

What is the average expected number of songs from this sample? (the mean of the probability distribution)

3.

What is the standard deviation of the number of songs from this sample? (the SD of the probability distribution)

4.

What number is at the 55th percentile? (You may round to a whole number for the answer)