Can a pretest on mathematics skills predict success in a statistics course? The 82 students in...

Can a pretest on mathematics skills predict success in a statistics course? The 82 students in an introductory statistics class took a pretest at the beginning of the semester. The least-squares regression line for predicting the score y on the final exam from the pretest score x was ŷ = 9.6 + 0.77x. The standard error of b1 was 0.44

(a) Test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative. (Round your test statistic to three decimal places and your P-value to four decimal places.)

t =

df =

P =

Conclusion

We reject H0 at the 5% significance level.

We do not reject H0 at the 5% significance level.

(b) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Explain your answer.

P =

Conclusion We could reject H0 at the 5% significance level.

We could not reject H0 at the 5% significance level.

Expert Solution

orchestra answered 2 years ago

Does a math pretest predict success? Can a pretest on mathematics skills predict success in a...

Does a math pretest predict success? Can a pretest on mathematics skills predict success in a statistics course? The 62 students in an introductory statistics class took a pretest at the beginning of the semester. The least-squares regression line for predicting the score y on the final exam from the pretest score x was y^=13.8+0.81x. The standard error of b1 was 0.43. (a) Test the null hypothesis that there is no linear relationship between the pretest score and the score...

Does a statistics course improve a student's mathematics skills,as measured by a national test? Suppose a...

Does a statistics course improve a student's mathematics skills,as measured by a national test? Suppose a random sample of 13 students takes the same national mathematics exam prior to enrolling in a stats course and just after completing the course. At a 1% level of significance determine whether the scores after the stats course are significantly higher than the scores before. Take the differences = before - after. Before After 430 465 485 475 520 535 360 410 440 425 500 505 425 450 470 480 515 520 430 430 450 460...

Lets say you wanted to predict success in a college course - that is, you wanted...

Lets say you wanted to predict success in a college course - that is, you wanted to isolate some variables that have a causal influence on good performance in class. What are some potential INDEPENDENT variables that you might manipulate in an experimental design to test their effect on the DEPENDENT variable of course performance?

Among 180 students of mathematical statistics, 82 did not attend the lecture. The results of the...

Among 180 students of mathematical statistics, 82 did not attend the lecture. The results of the quiz showed that among students who appeared at the lecture 70 students received a positive grade (all students who obtained a positive grade were 95). Examine the appropriate test whether the hypothesis that "passing the quiz is independent of whether the student attends classes" is correct. Assume a significance level of 0.05.

3. The Mathematics & Statistics department at Lancaster University claims that, on average, 25% of students...

3. The Mathematics & Statistics department at Lancaster University claims that, on average, 25% of students obtain a first class degree. A competitor university is interested in showing that this value is an overestimate. They randomly sample 82 graduates and find that 18 have a host class degree What are the assumptions for conducting a hypothesis test around this data? Are these satisfied? What is your null hypothesis? What is your alternative hypothesis? Calculate the p-value for the hypotheses you...

In a poll, 360 students were tested about their interests in mathematics and statistics, the results...

In a poll, 360 students were tested about their interests in mathematics and statistics, the results are presented in the table below. Please determine at 0.01 level of significance whether a student’s interest in mathematics and independent of his/her interest in statistics. Interest in statistics Interest in mathematics Low Average High Low 63 42 15 Average 58 61 31 High 14 47 29 In this scenario which chi-square test does he need to perform? Please construct the null and alternative...

Consider a population that consists of the 70 students enrolled in a statistics course at a...

Consider a population that consists of the 70 students enrolled in a statistics course at a large university. If the university registrar were to compile the grade point averages (GPAs) of all 70 students in the course and compute their average, the result would be a mean GPA of 2.98. Note that this average is unknown to anyone; to collect the GPA information would violate the confidentiality of the students’ academic records. Suppose that the professor who teaches the course...

The numerical course grades in a statistics course can be approximated by a normal model with...

The numerical course grades in a statistics course can be approximated by a normal model with a mean of 70 and a standard deviation of 10. The professor must convert the numerical grades to letter grades. She decides that she wants 10% A's, 30% B's, 40% C's, 15% D's, and 5% F's. a. What is the cutoff for an A grade? (Use 2 decimal places.) (Draw a picture!.) a. What is the cutoff for an B grade? (Use 2 decimal...

A sample of 10 students was selected from a large statistics course. The grades of the...

A sample of 10 students was selected from a large statistics course. The grades of the 10 students on their test are shown below: 94 61 96 66 92 68 75 85 84 78 3a. Create a histogram, with the first class being 60-69. (3 pts) 3b. Calculate the following for the above data. Please only report the results. (8 pts) Mean = _____ Median = _____ Mode = _____ Range = ____ 3c. Calculate the standard deviation for the...

1) Suppose the scores of students on a Statistics course are Normally distributed with a mean...

1) Suppose the scores of students on a Statistics course are Normally distributed with a mean of 542 and a standard deviation of 98. What percentage of the students scored between 542 and 738 on the exam? (Give your answer to 3 significant figures.) 2) A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard...

Question