The final test for this statistics class is worth 200 points. Out of 160 student

Question

The final test for this statistics class is worth 200 points. Out of 160 students who have taken the exam, the sample mean is 135.3 and the sample standard deviation is 37.9. To get at least a C on the final test, a student needs at least 70% (that is 140 points). At the 0.05 level of significance, test the claim that the mean score for the final test is greater than 140 points.

a) State the null and alternative hypotheses.

b) State the distribution that you will use.

c) Find the test statistic and use the appropriate variable.

d) Find the p-value.

e) Reject –or– Fail to Reject? Explain why!

f) State your actual conclusions in non-technical terms.

g) Construct a 90% confidence interval. Write your results in words.

I'm having the most trouble with F and G; if you could answer those, I'd greatly appreciate it!!

Explanation / Answer

a) null hypothesis: mean=140

alternative hypothesis: mean>140

b) as we do not know population std deviation,we should use t distribution

c) std error of mean =std deviation/(n)1/2 =2.996

hence test stat =(X-mean)/std error =(135.3-140)/2.996 =-1.5686

d)for above p value =0.9406

e) do not reject as p value is higher then 0.05 level

f) we do not have sufficient evidence to conclude that the mean score for the final test is greater than 140 points

g) for 90% CI, t=1.6545

hence 90% confidence intrerval =sample mean -/+ t*Std error =130.3427 ; 140.2573

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