A UW Madison professor is interested in learning about the variance of grades for university students. The professor gathers the sample variance for a random sample of 50 students. From past experience, the professor knows that the population of students is normally distributed. The sample variance that is collected is equal to 80. The professor would like to infer at the 1% significance level that the population variance is less than 100. a. State the appropriate null and alternative hypothesis.
b. What is the correct test statistic?
c. What is the conclusion of the test?
d. What would be the effect if the professor increased the sample size?

A) H0 : μ = 100  

   H1 :  μ < 100

B)  39.2

C)  We fail to reject null hypothesis

D) If the professor increases the sample size the value of the test statistic will increase .

Step-by-step explanation:

sample variance ( s ) = 80

sample size = 50

At ∝ = 0.01  population variance ( σ )   < 100

a) Hypothesis

H0 : μ = 100  ( Null hypothesis )

H1 :  μ < 100  ( Alternate hypothesis )

b) Determine The correct test statistic

x^2 = ( n-1 ) * s^2/σ^2

      = ( 49 ) * 80^2 / 100^2

      = 39.2

C) Determine the conclusion of the test

The P-value = 0.1596  ( calculated )

The conclusion of the test is that we fail to reject null hypothesis given that

P-value ( 0.1596 ) > ∝ ( 0.01 )  

D) If the professor increases the sample size the value of the test statistic will increase .

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

the answer to this question is 3/19

step-by-step explanation: