In a survey of 700 community college students, 481 indicated that they have read a book...

In a survey of 700 community college students, 481 indicated that they have read a book for personal enjoyment during the school year (based on data from the Community College Survey of Student Engagement).
1. Determine a 90% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year. You must show your work. Round the limits to the nearest thousandth.
1. For a 90% confidence interval, would it be unusual if less than 450 students indicated that they have read a book for personal enjoyment during the school year? Justify your answer.
1. For a 99% confidence interval, would it be unusual if less than 450 students indicated that they have read a book for personal enjoyment during the school year? Justify your answer.

Solutions

Expert Solution

Here, = 481/700 = 0.6871

a) In general, (1-)% confidence interval for the population proportion is obtained as follows :

where Z (/2) = Z (0.05) = 1.6449

Thus, 90% confidence interval for the population proportion is:

( 0.6583 , 0.7159 )
( 460.81, 501.149 ) (Here n = 700 is multiplied to the above 90% CI )

b) Since the 90% confidence interval for the population proportion does not contains values less than 450, it would be unusual if less than 450 students indicated that they have read a book for personal enjoyment during the school year.

c) 99% confidence interval for the population proportion is:

( 0.6420, 0.7322 )
( 449.400, 512.540 ) (Here n = 700 is multiplied to the above 90% CI )
Since the 99% confidence interval for the population proportion does contains values less than 450, it would not be unusual if less than 450 students indicated that they have read a book for personal enjoyment during the school year.

Hope this answers your query!

orchestra answered 1 year ago

Next > < Previous

Related Solutions

In a survey of 650 community college students, 423 indicated that they have read a book...

In a survey of 650 community college students, 423 indicated that they have read a book for personal enjoyment during the school year. Construct a 90% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year. Use 4 non-zero decimal places in your calculations. a.Verify the normality condition and the independence condition b.Find the Z-alpha/2 c.Find the margin of error (ME) d. Find the upper/lower bound and Interpret the...

In a recent survey of 150 students at a large community college, 86 students said they...

In a recent survey of 150 students at a large community college, 86 students said they were “regular” coffee drinkers. It is known that 64% of all students at that community college are “regular” coffee drinkers. Use this information to compute necessary quantities, and fill in the blanks: The average distance between the values of the sample proportion (from all possible random samples of 150 students from this community college) of "regular" coffee drinkers and the population proportion 0.64 of...

A librarian claims that the mean number of books read per month by community college students...

A librarian claims that the mean number of books read per month by community college students is less than 2 books. A random sample of 28 community college student had read a mean of 2 books with a standard deviation of 2.14 books. Test the librarian’s claim at the 0.01 level of significance. State the hypotheses and identify the claim. Find the critical value(s) Compute the test value. Make the decision to reject or not reject the null hypothesis. Summarize...

A survey was conducted to see if community college students preferred asynchronous distance learning (where learningoccurs...

A survey was conducted to see if community college students preferred asynchronous distance learning (where learningoccurs through online channels without real-time interaction) or synchronous distance learning (where learning happens in real time, perhaps on Skype or Zoom). Of the 250 students surveyed, 100 preferred asynchronous distance learning and 150 preferred synchronous distance learning. Construct a 95% confidence interval for the proportion of students who prefer asynchronous distance learning. The local newspaper reported on the results of the survey by saying...

A college administrator wants to survey 250 students that attend her college to see if students...

A college administrator wants to survey 250 students that attend her college to see if students are satisfied with the course offerings. Match the strategies to their corresponding sampling techniques. The administrator stands by the front door of the admissions department and asks the first 250 students who walk in. The administrator researches the ethnic make-up of the college and makes sure that the proportion of each ethnic group represented in the sample is the same as the corresponding proportion...

2. A simple random sample of 1oo community college students was selected from alarge community college....

2. A simple random sample of 1oo community college students was selected from alarge community college. The gender of each student was recorded, and each student was asked the following questions. 1. Have you ever had a part time job? 2. If you answered yes to the previous question, was your part-time job in the summer only? The responses are summarized in the table below. Job Experience · 'iINever had a part-time job F· -------··-·- -~--·-····- ---·---· -·--- ---- ....

3. The population of male students at Gallup (NM) Community College have a men height of...

3. The population of male students at Gallup (NM) Community College have a men height of 67.5 inches. It is claimed that male students who try out for the basketball team are taller than the general population of male students. To test this claim a sample of n= 36 male students who try out for the basketball team have a mean height of 68.3 inches and a standard deviation of 2.8 inches. Test this claim at the 90 and 99%...

2.5 7.In a survey of college students, each of the following was found. Of these students,...

2.5 7.In a survey of college students, each of the following was found. Of these students, 356356 owned a tablet, 294294 owned a laptop, 280280 owned a gaming system, 195195 owned a tablet and a laptop, 199199 owned a tablet and a gaming system, 137137 owned a laptop and a gaming system, 6868 owned a tablet, a laptop, and a gaming system, and 2626 owned none of these devices. Complete parts a) through e) below. a) How many college students...

Do College students who have volunteered for community service work differ from those who have not?...

Do College students who have volunteered for community service work differ from those who have not? A study obtained data from 57 students who had done service work and 17 who had not. One of the response variables was a measure of attachment to friends, measured by the Inventory of Parent and Peer Attachment. Here are the results. Group Condition n x s__ 1 Service 57 105.32 14.68 2 No Service 17 96.82 14.26 a. Do these data give evidence...

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...

Subjects