Question

The average reading speed of adult Americans is claimed to be 250 words per minute. The English department of a major American research university believes that this is not the case. They conduct a study using a simple random sample of 74 adult Americans and find an average reading speed of 280 words per minute. Assume the population standard deviation is know to be 25 words per minute. Given the above information answer the following questions.
Looking for null and alternative hypotheses, test statistic, and is there sufficient evidence to support researcher's claim at .01 level of significance?

Answer 1

Solution :

Given that,

Population mean = = 250

Sample mean = = 280

Population standard deviation = = 25

Sample size = n = 74

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 250

Ha: 250

The test statistics,

Z =( - )/ (/n)

= ( 280 - 250 ) / ( 25 / 74 )

= 10.32

P- Value = 2*P(Z > z )

= 2 * ( 1 - P(Z < 10.32 ))

= 2 * ( 1 - 1 )

= 0.00

The p-value is p = 0, and since p = 0 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough sufficient evidence to the average reading speed of adult Americans is claimed to be 250 words per minute, at the 0.01 significance level.