Question

1: Sample:   

Gender	Verbal	Math
f	630	660
m	610	550
f	680	660
m	490	390
f	510	520
m	700	700
f	640	710
f	520	470
f	530	500
m	640	570
f	710	700
f	630	520
f	670	580
f	630	610
m	360	290
f	540	490
f	490	560
m	730	760
m	760	700
f	530	670
m	710	700
f	630	610
f	530	490
f	420	410
f	490	510

- (b) Now find the mean and standard deviation of this sample (for SAT-Math Scores). Please show your work;

For question 2: -

(c) Use your sample to create a 95% confidence interval for the population mean of SAT-Math scores at this high school. Explain this process…use both “math” (e.g, symbols, pictures, numbers, etc) and writing to explain your process. ALSO explain what this indicates! (In other words, interpret the meaning). (Be careful with z- vs. t- scores!) -

(d) Based on your confidence interval, compare the Math performance of these students at this school with the statewide mean Math score of 503 (Consider 503 to be the population mean). Offer a brief answer to the question: “How do students’ SAT Math scores stack up against the rest of the state?”

For question 3: -

(e) Moving on…and this is a bit different…determine whether a sample provides statistical evidence that Verbal and Math scores differ for students at this high school. Yes, this is hypothesis testing! Again, you are using the 0.05 significance level.

1.

M/F	Verbal	Math
f	450	450
f	640	540
f	630	610
f	660	720
f	590	640
f	500	540
f	480	360
f	450	420
f	620	600
f	710	720
m	590	570
m	400	400
m	600	590
m	610	610
m	660	570
m	580	650
m	530	520
m	690	640
m	480	570
m	650	650

2. You will now have two lists of values, the Math and Verbal, for these 20 students. You will find the difference of the scores as part of the paried t test. Thus, you have one list of values— the “difference.”

3. Naturally, you will need to calculate the mean and sample standard deviation for this set of “differences” (again, the book will help).

4. I suggest you have the null hypothesis be that there is no significant mean difference between the Math scores and the Verbal scores of students at this high school. The alternative hypothesis is that there is a significant mean difference between the Math scores and Verbal scores at this high school.

5. Clearly document your process and “write up” the answer to: Is there a significant difference between Verbal and Math scores for these students?

Answer 1

(b)

(d) The Math performance of these students at this school with the statewide mean is Math score of 503 (Consider 503 to be the population mean). Since 95% Confidence interval for population mean of math score is (525.1,621.3). Hence the statewide mean is Math score is less than the lower boundary of the confidence interval. Hence the Math performance of the students at this school is higher than the students of the rest of the state.

Hence we conclude that there is no significant mean difference between the Math scores and Verbal scores at this high school.