![georgesarkes12](/avatars/45775.jpg)
georgesarkes12
18.07.2020 •
Mathematics
It is reported that 230 out of 600 middle school boys plan to see the new Captain Marvel movie. Find a 90% confidence interval estimate for the percentage of all middle school boys planning to see the movie. The movie theater claims that 25% of all middle school boys are planning to see the movie. Does their claim appear to be correct?
Solved
Show answers
More tips
- C Computers and Internet How to Download Movies from Torrents?...
- S Style and Beauty How to Sew Harem Pants?...
- C Computers and Internet Е-head: How it Simplifies Life for Users?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
Answers on questions: Mathematics
- M Mathematics A shopkeeper bought wheat for rs.35000. Due to leakage in the godown 1/7 of the total wheat was spoiled. He sold the good wheat at a gain of 10% and the spoiled when at a loss of...
- M Mathematics Anyone? please help!...
- M Mathematics Someone please help me!!!...
- M Mathematics Solve for the value of n....
- M Mathematics What is the average rate of change on the interval [-5,-3)? g(x) = -VX + 6 – 3...
- M Mathematics Make a conjecture about the next term in the sequence: 0.5, -1, 2, -4 *...
- M Mathematics The number of stay-at-home fathers in Canada went from 20,610 in 1976 to 53,555 in 2 010. The growth seems fairly linear. Predict the number of stay-at-home fathers in Canada for...
- M Mathematics PLEASE SAVE ME FROM FAILING ( PICTURE BELOW)...
- M Mathematics Simplify: -8 (4a-3b)=...
- M Mathematics What is the total amount, in cups, of four required for each cup of chocplate using this cake recipe?...
Ответ:
A 90% confidence interval estimate for the percentage of all middle school boys planning to see the movie is [0.350, 0.416].
Step-by-step explanation:
We are given that it is reported that 230 out of 600 middle school boys plan to see the new Captain Marvel movie.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. =
~ N(0,1)
where,
= sample proportion of middle school boys who plan to see the new Captain Marvel movie =
= 0.383
n = sample of middle school boys = 600
p = population proportion
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
So, 90% confidence interval for the population proportion, p is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 <
< 1.645) = 0.90
P(
<
<
) = 0.90
P(
< p <
) = 0.90
90% confidence interval for p = [
,
]
= [
,
]
= [0.350, 0.416]
Therefore, a 90% confidence interval estimate for the percentage of all middle school boys planning to see the movie is [0.350, 0.416].
The claim of the movie theater that 25% of all middle school boys are planning to see the movie is incorrect because in the above interval 25% value is not included, that is between 35% and 42% middle school boys are planning to see the movie.
Ответ: