Question

Note: All of the data sets associated with these questions are missing, but the questions themselves are included here for reference. Large Data Set 1 records the SAT scores of 1,000 students. Regarding it as a random sample of all high school students, use it to test the hypothesis that the population mean exceeds 1,510, at the 1% level of significance. (The null hypothesis is that μ = 1510.) answer: H0:μ=1510H0:μ=1510 vs. Ha:μ>1510.Ha:μ>1510. Test Statistic: Z = 2.7882. Rejection Region: [2.33,∞).[2.33,∞). Decision: Reject H0. who could explain the answer step by step, please, how did they find test stat value and critical value?

Answer 1

Solution:

z test for mean

Ho::μ=1510

Ha:μ>1510

alpha=1%=0.01

test statistic is

z=xbar-mu/sigma/sqrt(n)

=xbar-1510/sigma/sqrt(1000)

sample mean not provided

population standard deviation not given.

But given final test statistic as z=2.7882

z crit for 1%=2.33

since z statistic is greater than critical z value

Reject null hypothesis.

so,Accept alternative hypothesis.

Conclusion

There is sufficient statistical evidence at 5% level of significance to conclude that  the population mean exceeds 1510.