Question

Note: All of the data sets associated with these questions are missing, but the questions themselves...

Note: All of the data sets associated with these questions are missing, but the questions themselves are included here for reference.

  1. 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?

Math   Statistics-And-Probability   
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Homework Answers

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.

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