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Question: A researcher collected data from a random sample of 25 high school freshmen and found the mean of...

A researcher collected data from a random sample of 25 high school freshmen and found the mean of the sample to be 85.40 on the Test of Critical Thinking (TCT). She also calculated the standard deviation from the sample and discovered the value was 12.30. The average score on the Test of Critical Thinking for all high school seniors in a large school district is 90.00. The researcher wants to know if the mean TCT of the 25 high school freshmen in the random sample is different from the population’s (i.e., high school seniors) TCT mean.

e.What decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis?
f. Construct a 95% confidence interval around the sample mean of 85.40. Does this confidence interval contain the population mean of 90.00?
g. Provide a brief conclusion regarding your findings. Use your powerpoint lecture slides for writing out the interpretation of your results.
[ME: What decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis? (10p) e. f. Construct a 95% confidence interval around the sample mean of gaps. Does this confidence interval contain the population mean of 90.00? (Extra credit:10p) Provide a brief conclusion regarding your findings. Use your powerpoint lecture slides for writing out the interpretation of your results. (10p) g.]

Answer 1

a) H₀: = 90

    H₁: 90

The test statistic t = ()/(s/)

                             = (85.4 - 90)/(12.3/)

                             = -1.87

At alpha = 0.05, the critical values are t_{0.025, 24} = +/- 2.064

Since the test statistic value is not less than the lower critical value(-1.87 > -2.064), so we should not reject the null hypothesis.

f) The 95% confidence interval for population mean is

+/- t_{0.025, 24} * s/

= 85.4 +/- 2.064 * 12.3/

= 85.4 +/- 5.077

= 80.323, 90.477

Yes, the confidence interval cointain the population mean of 90.

g) There is not sufficient evidence to conclude that the mean TCT of the 25 high school freshmen in the random sample is different from the population's TCT mean.