Question

Suppose the national reading level for high school students 120 words per minute with a standard deviation of 14. A local high school wants to know their students read at a level different from the national average. The level of the test is set at 20. A random sample size of 122 students has been drawn and the resulting average is 130 words per minute. Provide the critical value, test statistia and the number of this hypothesis test has. Show Work

Answer 1

Answer)

Null hypothesis Ho : u = 120.

Alternate hypothesis Ha : u not equal to 120.

As the population s.d is known here we can use standard normal z table to estimate the test.

Alpha = 0.2.

As here we have two tailed test we will first divide the alpha into two parts.

0.2/2

= 0.1

From z table, P(z<-1.282) = P(z>1.282) = 0.1

Critical values are -1.282 and 1.282 respectively,

Rejection region is greater than 1.282 and less than -1.282.

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (130 - 120)/(14/√122) = 7.89.

Since the obtained test statistics is greater than 1.282.

Reject Ho.

We have enough evidence to conclude that students read at a level different from the national average.