Please do this in Rstudio (R code). In a class survey, students are asked how ma

Question

Please do this in Rstudio (R code).

In a class survey, students are asked how many hours they sleep per night. In the sample of 22 students, the mean was 5.77 hours with a standard deviation of 1.572 hours. The parameter of interest is the mean number of hours slept per night in the population from which this sample was drawn. (a) Which kind of confidence intervals is appropriate to use here, z-interval or t-interval? (b) Please use R to find the critical value they need when constructing a 98% CI. (c) Please use R to construct a 98% CI for the mean number of hours slept per night. (d) Please use R to construct a 98% lower confidence bound for the mean number of hours slept per night.

Explanation / Answer

Answer:

a). t interval

b).

R code:

n <- 22

t<- qt(0.99,df=n-1)

t

[1] 2.517648

c).

R code:

# 98% CI for mean

a <- 5.77

s <- 1.572

n <- 22

error <- qt(0.99,df=n-1)*s/sqrt(n)

left <- a-error

right <- a+error

left

right

R output:

[1] 4.926206

> right

[1] 6.613794

98% CI = (4.926206, 6.613794)

d).

R code:

# 98% lower CI for mean

a <- 5.77

s <- 1.572

n <- 22

error <- qt(0.98,df=n-1)*s/sqrt(n)

left <- a-error

left

R output:

5.03621

98% lower bound= 5.03621

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