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Hypothesis Tests with Z-statistics The mean for the SATs for all high school students was 500,...

Hypothesis Tests with Z-statistics

The mean for the SATs for all high school students was 500, with a standard deviation of 100. 75 students from Rio Hondo were tested and they produced a mean of 510.

a. Who are the groups being compared/tested?
b. What are the null and research hypotheses?
c. what are the numbers needed for the z statistic?
d. What is the z statistic?
e. For a two tailed test at .05 significance, the critical area is +/- 1.96. What decision do we make?
e. For a two tailed test at .05 significance, the cutoff is +/- 1.96, what decision do we make?

Math   Statistics-And-Probability   
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Answer #1

a. Who are the groups being compared/tested?

Answer:

A group of 75 students from Rio Hondo were tested.

b. What are the null and research hypotheses?

Null hypothesis: H0: The mean for the SATs for all high school students was 500.

Alternative hypothesis: Ha: The mean for the SATs for all high school students was not 500.

c. what are the numbers needed for the z statistic?

From given data, we have

µ = 500

Xbar = 510

σ = 100

n = 75

d. What is the z statistic?

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (510 - 500)/[100/sqrt(75)]

Z = 0.8660

e. For a two tailed test at .05 significance, the critical area is +/- 1.96. What decision do we make?

We do not reject the null hypothesis, because test statistic Z value lies between -1.96 and 1.96.

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