The president of a university claimed that the entering class this year appeared

Question

The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university’s record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance.

What are the null and alternative hypotheses?

What is the probability of making a Type I error the president wants to use?

Cannot be determined.

0.025

0.95

0.05

Which test should be used?

t-test for the population mean.

Z test for the population mean.

Z test for the population proportion.

You will reject the null hypothesis if the calculated value of the test statistic is:

less than -1.73

less than -1.96 OR greater than 1.96

less than -2.09 OR greater than 2.09

less than -1.64

What is the calculated value of the test statistic? Round your answer to 2 decimal places.

Explanation / Answer

1) NULL hypothesis: mean =1520

alternate hypothesis: mean <1520

probability of making a Type I error the president wants to use =0.05

Which test should be used : t-test for the population mean.

You will reject the null hypothesis if the calculated value of the test statistic is: =less than -1.73

here std error -std deviation/(n)1/2 =11.85

hence test stat =(X-mean)/std error =(1501-1520)/11.85 =-1.60

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