Question

1. 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 was440. Compare this sample to the population of SAT verbal test scores (SAT Verbal Test μ = 430 and σ = 120).

1. Calculate the standard error of the mean.

2. Calculate z_observed

3. State the null hypothesis using the names of the variable and sample(Ho)

4. State the alternative hypothesis Ha

5. What is the probability of finding this difference or more extreme if the null hypothesis is true? Hint: look at the proportion of the area under the curve in the nearest tail.

Answer 1

a) Given n= sample size = 100 , xbar = 440 , = 430 , = 120.

The standard error of sample mean = /√n = 120/√100

Standard error = 12

b) Z_{​​​​​​observed} = ( xbar - )/(/√n) = (440 - 430)/12

Zobserved = 0.83

c) Null hypothesis is population mean of SAT score is 430, H Ho : = 430

d) alternative hypothesis H1 : 430 , i.e verbal SAT score is different than 430.