a. 1. In a sample of n = 91 randomly selected men, x = 27 were observed to be left-handed. Construct a 95% confidence interval for the true proportion of men who are left-handed. We must first get our point estimate for the true proportion of left handed men and then use knowledge from class and labs to build that confidence interval using the general form: [point estimate] +/- [critical value]*[standard error] phat < 27/91 z_cv <- qnorm (1-0.05/2) # Critical value from N (0,1) se.ci <- sqrt (phat* (1-phat)/91) # se based on phat for CI b. Suppose it is believed that the proportion of left-handedness among males is 23%. Formally test whether our sample is aligned with previous research (Ho: p=0.23 vs. H₁: p‡0.23) at the a=0.05 significance level. (A "formal" test means to do ALL steps - yes, even the hypotheses & conclusion!!) NOTE: The standard error for hypothesis tests of a proportion is different than the confidence interval! se.ht <- sqrt((0.23* (1-0.23))/91) # se based on p0 for hyp test z.star < (phat 0.23)/se.ht Now calculate the p-value and/or critical value(s) using the normal distribution functions pnorm () or qnorm(), respectively, come to a decision and state your conclusion in the context of the problem. Coding Tips! There's an R function similar to t.test named prop. test used to test proportions! prop.test(x = # successes, n = # trials, p = po, alternative = c("two.sided", "greater", "less"), conf.level = 1-alpha, correct = FALSE) IMPORTANT: We must set correct = FA SE in order for the output to match what we just did! c. Use the R function above to check your answers! prop.test(x = 27, n = 91, p=0.23, alternative="two.sided", conf.level = 0.95, correct=FALSE)
a. 1. In a sample of n = 91 randomly selected men, x = 27 were observed to be left-handed. Construct a 95% confidence interval for the true proportion of men who are left-handed. We must first get our point estimate for the true proportion of left handed men and then use knowledge from class and labs to build that confidence interval using the general form: [point estimate] +/- [critical value]*[standard error] phat < 27/91 z_cv <- qnorm (1-0.05/2) # Critical value from N (0,1) se.ci <- sqrt (phat* (1-phat)/91) # se based on phat for CI b. Suppose it is believed that the proportion of left-handedness among males is 23%. Formally test whether our sample is aligned with previous research (Ho: p=0.23 vs. H₁: p‡0.23) at the a=0.05 significance level. (A "formal" test means to do ALL steps - yes, even the hypotheses & conclusion!!) NOTE: The standard error for hypothesis tests of a proportion is different than the confidence interval! se.ht <- sqrt((0.23* (1-0.23))/91) # se based on p0 for hyp test z.star < (phat 0.23)/se.ht Now calculate the p-value and/or critical value(s) using the normal distribution functions pnorm () or qnorm(), respectively, come to a decision and state your conclusion in the context of the problem. Coding Tips! There's an R function similar to t.test named prop. test used to test proportions! prop.test(x = # successes, n = # trials, p = po, alternative = c("two.sided", "greater", "less"), conf.level = 1-alpha, correct = FALSE) IMPORTANT: We must set correct = FA SE in order for the output to match what we just did! c. Use the R function above to check your answers! prop.test(x = 27, n = 91, p=0.23, alternative="two.sided", conf.level = 0.95, correct=FALSE)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![1. In a sample of n = 91 randomly selected men, x = 27 were observed to be left-handed.
a. Construct a 95% confidence interval for the true proportion of men who are left-handed.
We must first get our point estimate for the true proportion of left handed men and then use knowledge
from class and labs to build that confidence interval using the general form:
[point estimate] +/- [critical value]*[standard error]
phat < 27/91
z_cv <- qnorm (1-0.05/2)
#Critical value from N (0,1)
se.ci <- sqrt (phat* (1-phat)/91) # se based on phat for CI
b. Suppose it is believed that the proportion of left-handedness among males is 23%. Formally test whether
our sample is aligned with previous research (H₁: p=0.23 vs. H₁: p‡0.23) at the a=0.05 significance
level. (A "formal" test means to do ALL steps - yes, even the hypotheses & conclusion!!)
NOTE: The standard error for hypothesis tests of a proportion is different than the confidence interval!
se.ht <- sqrt((0.23* (1-0.23))/91) # se based on p0 for hyp test
z.star <- (phat - 0.23)/se.ht
Now calculate the p-value and/or critical value(s) using the normal distribution functions pnorm () or
qnorm (), respectively, come to a decision and state your conclusion in the context of the problem.
Coding Tips!
There's an R function similar to t.test named prop. test used to test proportions!
prop.test (x #successes, n = # trials, p = p0,
=
alternative =
conf.level
c("two.sided”, “greater", “less"),
=
= 1-alpha, correct
FALSE)
FALSE in order for the output to match what we just did!
IMPORTANT: We must set correct
=
c. Use the R function above to check your answers!
prop.test (x
=
=
27, n 91, p=0.23, alternative="two.sided",
conf.level 0.95, correct=FALSE)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49425756-a161-4845-94fd-16236bd2737c%2F3f9d619c-69ed-4204-a869-366771cd8558%2Fpaascu_processed.png&w=3840&q=75)
Transcribed Image Text:1. In a sample of n = 91 randomly selected men, x = 27 were observed to be left-handed.
a. Construct a 95% confidence interval for the true proportion of men who are left-handed.
We must first get our point estimate for the true proportion of left handed men and then use knowledge
from class and labs to build that confidence interval using the general form:
[point estimate] +/- [critical value]*[standard error]
phat < 27/91
z_cv <- qnorm (1-0.05/2)
#Critical value from N (0,1)
se.ci <- sqrt (phat* (1-phat)/91) # se based on phat for CI
b. Suppose it is believed that the proportion of left-handedness among males is 23%. Formally test whether
our sample is aligned with previous research (H₁: p=0.23 vs. H₁: p‡0.23) at the a=0.05 significance
level. (A "formal" test means to do ALL steps - yes, even the hypotheses & conclusion!!)
NOTE: The standard error for hypothesis tests of a proportion is different than the confidence interval!
se.ht <- sqrt((0.23* (1-0.23))/91) # se based on p0 for hyp test
z.star <- (phat - 0.23)/se.ht
Now calculate the p-value and/or critical value(s) using the normal distribution functions pnorm () or
qnorm (), respectively, come to a decision and state your conclusion in the context of the problem.
Coding Tips!
There's an R function similar to t.test named prop. test used to test proportions!
prop.test (x #successes, n = # trials, p = p0,
=
alternative =
conf.level
c("two.sided”, “greater", “less"),
=
= 1-alpha, correct
FALSE)
FALSE in order for the output to match what we just did!
IMPORTANT: We must set correct
=
c. Use the R function above to check your answers!
prop.test (x
=
=
27, n 91, p=0.23, alternative="two.sided",
conf.level 0.95, correct=FALSE)
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