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One-hundred test scores were recently obtained from a local high school to compare to the national...

One-hundred test scores were recently obtained from a local high school to compare to the national average. The mean verbal SAT score for this sample was 440. Compare this sample to the population of SAT verbal test scores (SAT Verbal Test μ = 430 and σ = 120).

State the alternative hypothesis Ha

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Null hypothesis Ho : u = 430

Alternate hypothesis Ha : u not equal to 430

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

Z = (440-430)/(120/√100) = 0.83

As the population s.d is known here we will use z distribution table to estimate the p-value

From z table, P(z>0.83) = 0.2033

As the test is two tailed, P-value = 2*0.2033 = 0.4066

As the obtained P-value is extremely large we fail to reject the null hypothesis

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