Question

In: Statistics and Probability

Professor Venkat is on a mission to find out the average number of students absent from...

Professor Venkat is on a mission to find out the average number of students absent from his lectures. For this, he analyzed 14 random attendance sheets from his previous semesters and found out that on average, the number of absentees was 38 with a standard deviation of 12. Let's assume that the data follows a Gaussian distribution. Construct a 99% confidence interval for the true mean of the dataset.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 38

sample standard deviation = s = 12

sample size = n = 14

Degrees of freedom = df = n - 1 = 13

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,24 = 3.012

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

= 3.012 * (12 / $\sqrt$ 14)

= 9.660

The 99% confidence interval estimate of the population mean is,

- E < < + E

38 - 9.660 < < 38 + 9.660

28.340 < < 47.660

A 99% confidence interval for the true mean of the dataset is ,

(28.340 , 47.660)

orchestra answered 1 year ago

Consider the number of days absent from a random sample of six students during a semester:...

Consider the number of days absent from a random sample of six students during a semester: A= {2, 3, 2, 4, 2, 5} Compute the arithmetic mean, geometric mean, median, and mode by hand and verify the results using R Arithmetic Mean: X=i=1nXin=2+3+2+4+2+56=3 mean(data2$absent) [1] 3 Geometic Mean: GMx=Πi=1nX11n=2∙3∙2∙4∙2∙516=2.79816 >gmean <- prod(data2$absent)^(1/length(data2$absent)) > gmean [1] 2.798166 Median: X=12n+1th, Xi2,2,2,3,4,5, n=6=126+1th ranked value=3.5, value=2.5 days absent >median(data2$absent) [1] 2.5 Mode: Most frequent value=2 > mode <- names(table(data2$absent)) [table(data2$absent)==max(table(data2$absent))] > mode [1]...

The table below shows the number of students absent on the particular day of the week:...

The table below shows the number of students absent on the particular day of the week: Day M Tu W Th F Number 111 80 85 94 99 Test if the distribution of students absent is uniform through the week with the significance level of 5%.

A history class has 75 members. If there is a 12% absentee rate per class meeting, find the mean, variance, and standard deviation of the number of students who will be absent from each class.

A biology professor claims that, on the average, 10% of her students get a grade of...

A biology professor claims that, on the average, 10% of her students get a grade of A, 30% get a B, 40% get a C, 10% get a D, and 10% get an F. The grades of a random sample of 100 students were recorded. The following table presents the results. Grade A B C D F Observed 10 34 46 6 4 Test the hypothesis that the grades follow the distribution claimed by the professor. Use the α =...

A professor thinks that the mean number of hours that students study the night before a...

A professor thinks that the mean number of hours that students study the night before a test is 1.75. He selected a random sample of 12 students and found that the mean number of study hours was 2.44 and the standard deviation is 1.26 hours. Test the professor’s claim at α = 0.01. a 1-6) Give the hypotheses for H0 (a1, a2 and a3) and H1 (a4, a5 and a6) H0 a1) µ or p a2) =, ≥, ≤ a3)...

3. a. A sample of 38 students from a community college reveals the average number of...

3. a. A sample of 38 students from a community college reveals the average number of units they are taking is 11.5, with a standard deviation of 1.4. Determine a 98% confidence interval for the true mean. b. Assume now that the same results occurred from a sample of size 9, but it was known that the original population was normal. c. Repeat problem 3a, assuming that the standard deviation was the real population standard deviation.

Data was collected from students to determine the effects on overall grade average and number of...

Data was collected from students to determine the effects on overall grade average and number of hours spent playing video games per week. Grade Hours/Week 20 23 96 3 74 6 85 5 67 8 56 14 79 4 65 7 Which is the: -Independent variable? _______________________ -Dependent variable? _______________________ -Calculate the coefficient of correlation and interpret the results. -Determine both the coefficient of determination and non-determination and explain the result. -Determine the unrounded regression equation for this data set....

The president of a University wishes to find the average age of students presently enrolled. From...

The president of a University wishes to find the average age of students presently enrolled. From past studies, the standard deviation is known to be 2 years. A random sample of 50 students is selected and the mean is found to be 23.2 years. A. Find the 95% confidence interval for the population mean. B. Find the 99% confidence interval for the population mean?

According to the Chronicle of Higher Education, the average number of applications for an assistant professor...

According to the Chronicle of Higher Education, the average number of applications for an assistant professor position in US universities is 59.8, with a standard deviation of 13.6. A researcher thinks that the average number is actually less than 59.8, and his sample of 100 advertised positions at US universities produced a mean of 56.2 applicants. Test his claim, using a significance level of .05. Show all the steps (4 steps) discussed in the lecture video.

The average number of times Americans dine out in a week fell from 4.0 in 2008...

The average number of times Americans dine out in a week fell from 4.0 in 2008 to 3.8 in 2012 (Zagat.com, April 1, 2012). The number of times a sample of 20 families dines out last week provides the following data. 6 1 5 3 7 3 0 3 1 3 4 1 2 4 1 0 5 6 3 1 a) The skewness measure for these data is 0.34. Comment on the shape of the distribution. Is it the...