Question

In: Statistics and Probability

Students in a statistics class are conducting a survey to estimate the mean number of units...

Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 46 students. The mean of the sample is 12.5 units. The sample has a standard deviation of 1.8 units.

What is the 95% confidence interval for the average number of units that students in their college are enrolled in? Assume that the distribution of individual student enrollment units at this college is approximately normal.

( , )

Your answer should be rounded to 2 decimal places.

Expert Solution

Solution :

Given that,

= 12.5

s = 1.8

n = 46

Degrees of freedom = df = n - 1 = 46 - 1 = 45

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,45 = 2.014

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.014 * (1.8 / $\sqrt$ 46)

= 0.53

The 95% confidence interval estimate of the population mean is,

- E < < + E

12.5 - 0.53 < < 12.5 + 0.53

11.97 < < 13.03

(11.97 , 13.03)

orchestra answered 1 year ago

A study is conducted for students taking a statistics class. Several variables are recorded in the survey. The...

A study is conducted for students taking a statistics class. Several variables are recorded in the survey. The 300 students were asked what type of car the student owns, the number of credit hours taken during that semester, the time the student waited in line at the bookstore to pay for his/her textbooks, and the home state of the students. 1. Which of the following plots would be appropriate to graph the home states of the students? bar graph, histogram, scatter plot,...

Scores of students in a large Statistics class are normally distributed with a mean of 75...

Scores of students in a large Statistics class are normally distributed with a mean of 75 points and a standard deviation of 5 points. Find the probability that a student scores more than 80 points If 100 students are picked at random, how many do you expect to score below 70 points? If top 10% of students obtain an A grade, how much should a student obtain to get an A grade. Suppose four students are picked at random, find...

Find the sample size necessary to estimate the mean IQ score of statistics students such that...

Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is plus or minus3 IQ points of the true mean. Assume that the standard deviation is 15 and determine the required sample size. 2) In a survey of 2,416 adults, 1,876 reported that e-mails are easy to misinterpret, but only 1,231 reported that telephone conversations are easy to misinterpret. Complete parts (a) through...

Randomly selected students in a statistics class were asked to report the number of hours they...

Randomly selected students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. At α = 0.05. Can it be claimed that the scores on 2 tests are correlated on 0.01 significance level? Student #: 1 2 3 4 5 6 7 8 Test 1: 67 88 76 88 91 95 79 71 Test 2: 69 78 76 84 86 96 70 68

On a statistics test for a class of 40 students, the grades were normally distributed.The mean...

On a statistics test for a class of 40 students, the grades were normally distributed.The mean grade was 74, and the standard deviation was 8. 2. Janis scored 76 on this test. A. What was her z-score for this grade b. What percent of the class scored lower than Janis? c. Approximately how many students in the class scored lower than Janis? 3. The minumum passing grade on this test was 70. Approximately how many students scored lower than 70...

A statistics class for engineers consists of 53 students. The students in the class are classified...

A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table: College Major Sex Industrial Engineering Mechanical Engineering Electrical Engineering Civil Engineering Total Male 15 6 7 2 30 Female 10 4 3 6 23 Total 25 10 10 8 53 If a student is selected at random from the class by the instructor to answer a question, find the following...

Assume we want to estimate the mean IQ score for the population of statistics students. How...

Assume we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want to be 99% confident that the sample mean is within 5 IQ points of the true population mean? Consider the population’s standard deviation = 15.

2. According to survey data collected from 500 students in a recent Statistics class, the histogram...

2. According to survey data collected from 500 students in a recent Statistics class, the histogram for the number of hours of sleep they typically got per night is close to the normal curve with an average of 6.5 hours and a SD of 1.4 hours. a) Find percentage of students who sleep between 7 and 8 hours b) A student who sleeps 7 hours per night is at the _______th percentile of the score distribution c) Find the first...

A survey was conducted to estimate the mean number of books (denoted by µ) each university...

A survey was conducted to estimate the mean number of books (denoted by µ) each university student read in the last year. Among a random sample of 51 students, the number of books each student read in the last year was recorded. The sample mean was 8.039 and the sample standard deviation was 2.545. a. Write down the point estimate of µ. b. Calculate the standard error of the point estimate in a. c. To construct a 95% two-sided confidence...

In a simple random sample of 51 community college statistics students, the mean number of college...

In a simple random sample of 51 community college statistics students, the mean number of college credits completed was x=50.2 with standard deviation s = 8.3. Construct a 98% confidence interval for the mean number of college credits completed by community college statistics students. Verify that conditions have been satisfied: Simple random sample? n > 30? Find the appropriate critical value Since σ is unknown, use the student t distribution to find the critical value tα2 on table A-3 Degrees...