A math teacher claims that she has developed a review course that increases the

Question

A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with H-518. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean math score of the 1800 students is 525 with a standard deviation of 115. Complete parts (a) through (d) below (b) Test the hypothesis at the 0.10 level of significance. Is a mean math score of 525 statistically significantly higher than 518? Conduct a hypothesis test using the P-value approach. Find the test statistic. (Round to two decimal places as needed.) Find the P-value The P-value is (Round to three decimal places as needed.) ls the sample mean statistically significantly higher? O No O Yes

Explanation / Answer

Using minitab :

The command is Stat>>>Basic Statistics >>1 sample t...

Click on Summarized data

Sample size: 1800

Mean( that is sample mean) : 525

Standard deviation : 115

then click on Perform hypothesis test enter hypothesis mean (518 )

then click on Option select level of confidence = (1 - alpha )*100 = (1 - 0.10)*100= 90

Alternative " greater than"

Click on OK

Again click on OK

We get the following output

One-Sample T

Test of mu = 518 vs > 518

90% Lower
N Mean StDev SE Mean Bound T P
1800 525.00 115.00 2.71 521.52 2.58 0.005

from the above output

test statistic = t0 = 2.58

The p-value is = 0.005

Decision rule: 1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.005 < 0.10 so we used first rule.

That is we reject null hypothesis and accept alternative hypothesis.

So the sample mean is statistically significant.

So correct option is "Yes"

C) Even the test is statistically significance but increase in the mean score is only from 518 to 525 that is the test is not practically significant.

So correct option is "No, because the score bacame only 1.35% greater."

d) In this part only sample size change as n = 400 and all other values are same

Using Minitab we get the following output for part d)

One-Sample T

Test of mu = 518 vs > 518

90% Lower
N Mean StDev SE Mean Bound T P
400 525.00 115.00 5.75 517.62 1.22 0.112

Test statistic = t0 = 1.22

p-value = 0.112

For small sample size we fail to reject null hypothesis because here for n= 400 p-value = 0.112 > 0.10 and we fail to reject null hypothesis

So if we increase sample size then the likelihood of rejecting null hypothesis increases but large samples tend to

overemphasized practical insignificance difference.

so correct answer is A

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