Question

A researcher claims that the mean SAT scores is greater than 515. A sample of 1800 students shows the sample mean SAT scores is 519 and sample standard deviation is 111. Test the claim at 0.1 level of significance. (a) State the null and alternative hypotheses. (b) Calculate test statistic. (c) Find critical value. (d) Write a conclusion based on your results in part (b) and part (c).

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$$\leq$ 515

H_a : $\mu$ > 515

$\bar x$ = 519

$\mu$ = 515

s = 111

n = 1800

Test statistic = t = ($\bar x$ - $\mu$) / s / $\sqrt$n = (519 - 515) / 111 / $\sqrt$1800 = 1.53

Test statistic = 1.53

$\alpha$ = 0.1

Z_$\alpha$ = Z_0.1 = 1.28

Critical value = 1.28