all hypothesis testing problems must include the null and alternative hypotheses and report the p-value of the data.

A random sample of 45 students took an SAT preparation course prior to taking the SAT. The sample mean of their quantitative SAT scores was 575 with a s.d. of 90, and the sample mean of their verbal SAT scores was 530 with a s.d. of 110.
a) Construct 95% confidence intervals for the mean quantitative SAT and the mean verbal SAT scores of all students who take this course.
b) Construct 95% confidence intervals for the standard deviations of the QSAT and VSAT scores of all students who take this course.
c) What sample size would be needed to estimate the mean VSAT score with 95% confidence and with error of no more than 5 if it is assumed that the s.d. is no more than 110?
a) Suppose the mean scores for all students who took the SAT at that time was 535 for the quantitative and 505 for the verbal? Do the means for students who take this course differ from the means for all students at the 5% level of significance?

Chris is enrolled in a college algebra course and earned a score of 260 on a math placement test that was given on the first day of class. The instructor looked at two distributions of scores – one is the distribution for all first year college students who took the test, and the other is a distribution for students enrolled in this algebra class. Both are approximately normal and have the same mean, but the distribution for the algebra class has a smaller standard deviation. A z-score is calculated for Chris’ test score in both distributions (all first year college students and all algebra class students). Given that Chris’ score is well above the mean, which of the following would be true about these two z-scores?

a) The z-score based on the distribution for the algebra students would be higher.

b) The z-score based on the distribution for all first year college students would be higher.

c) The two z-scores would be the same.

d) There’s not enough information to answer this question.

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 1515 students, taught in traditional lab sessions, had a mean test score of 71.871.8 with a standard deviation of 6.16.1. A random sample of 1010 students, taught using interactive simulation software, had a mean test score of 84.384.3 with a standard deviation of 5.25.2. Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ1μ1 be the mean test score for the students taught in traditional lab sessions and μ2μ2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05α=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.

A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 17 American students had a mean height of 70 inches with a standard deviation of 1.73 inches. A random sample of 12 non-American students had a mean height of 66 inches with a standard deviation of 2.23 inches. Determine the 90% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to two decimal places.

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 13 students, taught in traditional lab sessions, had a mean test score of 76.1 with a standard deviation of 3.3 . A random sample of 19 students, taught using interactive simulation software, had a mean test score of 80.9 with a standard deviation of 4.9 . Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ 1 be the mean test score for the students taught in traditional lab sessions and μ 2 be the mean test score for students taught using interactive simulation software. 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.

Data collected from a local high school found that 18% of the students do not have internet access at home, which puts these students at a disadvantage academically. One teacher felt this estimate was too low and decided to test if the true percentage of students without home internet access was greater than the data suggested. To do this, she sampled 200 students. In her sample, 25% of the students did not have internet access at home. If the significance level for the hypothesis test is 1%, can the teacher conclude that more than 18% of all such students do not have internet access?

When answering the questions below

• make sure a decimal representation begins with 0, like this: 0.286
• if a test has two Critical Values, type it like this: -2.34 & 2.34
• round z values to 2 decimal places, and t values to 3 decimal places
• for the result, type either Reject, or Fail to Reject

Please type in the Critical Value(s) , the Test Statistic , and the result of the test

20. In a survey, three out of four students said that courts show too much concern for criminals. Of seventy randomly selected students

Would 68 be considered an unusually high number of students who feel that courts are partial to criminals?

21.

In a survey, three out of four students said that courts show too much concern for criminals. Of seventy randomly selected students

Would it be unusually low if we observed thirty of seventy students who feel that courts are partial to criminals?

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean ?=545.8μ=545.8 and standard deviation ?=28.4σ=28.4.

(a) What is the probability that a single student, randomly chosen from all those taking the test, would score 552 or higher?

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?

Mean: Standard deviation:

(c) What z-score corresponds to the mean score ?¯x¯ of 552?

(d) What is the probability that the mean score ?¯x¯ of these students is 552 or higher?

(e) Suppose that you want to test whether the mean SAT score is higher for students who take an SAT prep course. You take a random sample of 35 students who have taken an SAT prep course, and find that the sample mean score is 552. What is the p-value for this study?

A journal published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of several variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 10.1 hours and a standard deviation of 1.82 hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal.
Below what hours 90% of the visually impaired students have their sleep? [Answer to 2 decimal places]

A: 9.97   B: 12.43   C: 15.28   D: 16.05   E: 16.73   F: 18.30

What is the chance that a randomly selected visually impaired student has at least 8.5 hours of sleep? [Answer to 4 decimal places]

A: 0.0109   B: 0.2059   C: 0.3461   D: 0.6155   E: 0.8103   F: 0.9867

What is the inter-quartile range of sleep hours among visually impaired students. [Answer to 2 decimal places]

A: 2.35   B: 2.43   C: 2.46   D: 2.78   E: 2.85   F: 2.95

31. An instructor wants to test whether attending class influences how students perform on an
exam. There are 54 students in the class. There are 25 students who attended the class and passed
the exam, 6 students who attended class and failed the exam, 8 students who skipped the class and
passed the exam, 15 students who skipped the class and failed class. Please perform a statistical
test and indicate whether attending class influence the exam performance.

a) Parametric or nonparametric hypotheses?
b) Z distribution, t distribution, chi-square test or hypothesis test of a proportion
c) Please indicate the null hypotheses.
d) Please indicate the alternative hypotheses
e) Please calculate the stand error? (If it is a chi-square test, type NA for this question)
f) If z table will be used, type NA for this question. If t table will be used, indicate the degree of
freedom.
g) Please calculate the statistical value.
h) Hypothesis is supported or no supported, and what is your conclusion?