Question

What is the t score of the sample average of the following data, under the null hypothesis that the population average equals 63? Y = c(10, 24, 87, 42, 50)

a. 42.6

b. -20.4

c. -0.6961

d. -0.3113

e. -1.5566

Under the null hypothesis that the population average equals 63, what are the critical values for testing the null hypothesis if α = 0.01?

a. -4.6041 and 4.6041

b. -3.7469 and 3.7469

c. -2.7764 and 2.7764

d. -2.1318 and 2.1318

Construct a 99% confidence interval for the population mean.

a. (6.2127, 78.9873)

b. (14.6606, 70.5394)

c. (-17.74, 102.94)

d. (-92.3243, 177.5243)

e. (16.3886, 68.8114)

Answer 1

1)

x <- c(10,24,87,42,50)
> t.test(x,mu = 63)

        One Sample t-test

data:  x
t = -1.5566, df = 4, p-value = 0.1946
alternative hypothesis: true mean is not equal to 63
95 percent confidence interval:
  6.212677 78.987323
sample estimates:
mean of x 
     42.6 

option e) -1.5556 is correct

2)

df = n-1 = 4

qt(0.995,4)  

[1] 4.604095

option A) is correct

3)

t.test(x,mu = 63,conf.level = 0.99)

        One Sample t-test

data:  x
t = -1.5566, df = 4, p-value = 0.1946
alternative hypothesis: true mean is not equal to 63
99 percent confidence interval:
 -17.74 102.94
sample estimates:
mean of x 
     42.6 

99 percent confidence interval:
 -17.74 102.94

option C) is correct