Question

In: Statistics and Probability

Chris is enrolled in a college algebra course and earned a score of 260 on a...

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.

Expert Solution

It is given that there are two groups: one is all first year college students and all algebra class students.

Both the groups 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).

Also Chris’ score is well above the mean.

The z-score formula is,

Where x represents raw score, represents mean and represents standard deviation.

From the above formula, it is clear that if the standard deviation is larger than the z-score is smaller and if the standard deviation is smaller than the z-score is larger.

From the given information, it is clearly mentioned that the distribution for the algebra class has a smaller standard deviation. Therefore, it can be said that the z-score based on the distribution for the algebra students would be higher.

Hence, the correct option is a).

orchestra answered 2 years ago

Suppose that, for students who are enrolled in college algebra, 72 percent are freshman, 40 percent...

Suppose that, for students who are enrolled in college algebra, 72 percent are freshman, 40 percent are female, and 25 percent are female and freshman. Your answers should be entered as decimals and rounded to three decimal places. (A) one student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)? ___ (B) one student will be selected at random. What is the probability that the selected student will...

At the end of the second semester, Rita earned an B in the four-credit Algebra course,...

At the end of the second semester, Rita earned an B in the four-credit Algebra course, an A in the three-credit English course, an A in the 2-credit Language/Arts course, and a C in the three-credit Physics course. Using a four-point grade system, A is equivalent to four points, B is equivalent to three points, C is equivalent to two points, D is equivalent to one point, and F has no point. Calculate Rita's grade point average (GPA) for the...

Using R Studio: A College Algebra course requires students to take an assessment test at the...

Using R Studio: A College Algebra course requires students to take an assessment test at the start of the course and again at the end of the course. The pre and post test scores for ten students are: Student 1 2 3 4 5 6 7 8 9 10 Pre-test score 70 62 63 61 56 52 71 63 64 67 Post-test score 87 71 82 78 57 50 72 65 78 65 Do the assessment test results support the...

There are 2567 students enrolled at a small college, with 2053 of them enrolled in a...

There are 2567 students enrolled at a small college, with 2053 of them enrolled in a sociology course. In the sampling distribution of sample proportions of size 230, above what proportion will 52% of all sample proportions be? Select all answers that apply to your calculation below. Use the z-table given below to answer the question: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -0.2 0.421 0.417 0.413 0.409 0.405 0.401 0.397 0.394 0.390 0.386 -0.1 0.460...

Five students take statistics one semester and college algebra the next semester. Their overall course grades...

Five students take statistics one semester and college algebra the next semester. Their overall course grades (%) are listed in the table. Student Statistics College Algebra 1 80.0% 85.5% 2 72.6% 71.0% 3 99.0% 93.2% 4 91.3% 93.0% 5 68.9% 74.8% a. Which statistical procedure, listed in the Assessment, would be most appropriate to test the claim "student overall course grades are the same in both courses"? Options are: t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances...

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...

In the past, 60 % of all undergraduate students enrolled at state university earned their degrees...

In the past, 60 % of all undergraduate students enrolled at state university earned their degrees within four years of matriculation. a random sample of 95 students from the class that matriculated in the fall of 2012 was recently selected to test whether there has been a change in the proportion of students who graduate within four years. Administrators found that 40 of these 95 students graduated in the spring of 2016 (i,e. , four academic years after matriculation) ....

Consider the relationship between students’ score on a first course exam and their score on the...

Consider the relationship between students’ score on a first course exam and their score on the final exam. First-test score Final-exam score 153 145 144 140 162 145 149 170 127 145 118 175 158 170 153 160 Using (1) your calculator, a pencil and graph paper and then (2) Excel: Plot the data with the first-test score on the x axis and the final-exam score on the y axis. Find the arithmetic mean, the mean absolute deviation and...

The average exam score for students enrolled in statistics classes at Indiana University Northwest is 80...

The average exam score for students enrolled in statistics classes at Indiana University Northwest is 80 and grades are normally distributed. A professor decides to select a random sample of 25 students from his CJ statistics class to see how CJ students compare to the student body in terms of exam performance. The average exam score of this sample is 78 with a variance equal to 100. Are the stats exam scores of the students in the CJ class significantly...

A group of 100 of the 2,500 students enrolled in a college in natural sciences reveals...

A group of 100 of the 2,500 students enrolled in a college in natural sciences reveals that 35 are 17 years old, 45 are 18 years old, 10 are 19 years old, 6 are 20 years old, three are 21 years old and one is 22 years old. a)provide an estimate for the mean, variance and standard deviation for the Age of the group. b) Find the confidence interval with a confidence bands of 90% , 95% , and 99%...