Question

Suppose the national reading level for high school students is 140 words per minute with a standard deviation of 12. A local high school wants to know if 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 125 students has been drawn and the resulting average is 132 words per minute. Provide the critical value, the test statistic and the number of tails this hypothesis test has.

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Answer 1

Sol:

Null hypothesis Ho : u = 140.

Alternate hypothesis Ha : u not equal to 140

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 = (132 - 140)/(12/√125) = -7.45

Since the obtained test statistics is less than 1.282.

Do not Reject Ho.