(1) THIS PROBLEMthat involves calculating a 95% confidence interval.SHOW THE "E" SETUP & CALC.

High school students take the AP tests in different subject areas.This year 150 students took the biology exam of which 85 were female.And, 220 students took the calculus exam of which 100 were female.Calculate the difference in the PROPORTION of female students taking the biology exam verses female students taking the calculus exam using a 95% confidence level.

(2) THIS PROPORTION PROBLEMthat involves a hypothesis test at the 1% significance level.SHOW Z-Test SETUPAND Z-Critical value the z-Test was compared to.Also, use software to calculate the p-Value.Do both support the same conclusion?(they MUST).

Are more children diagnosed with Autism Spectrum Disorder in States that have urban areas over States that are mostly rural?In an urban State there were are 3003^rd grade students diagnosed with ASD out of 18,500 3^rd graders tested.In a rural state, there were 553^rd grade students diagnosed with ASD out of 2,3003^rd graders tested.Is there enough evidence to show that the proportion of children diagnosed with ASD in an urban State is more than the proportion in a rural State?Test at the = 1% level.

(3) THIS PROBLEMwhich is a basic TWO population means comparison hypothesis test (NOT a proportion problem - so we use t-values, not z-values).SHOW t-TEST SETUP and calculation,AND for the t-Critical, what SIGNIFICANCE LEVEL (the column) and whatdf (which row)were used and what the t-Critical value is.

Do people avoid driving on Friday the 13^th ?Here are data on 20 Fridays:10 on the 13^th and the other 10 on the Friday before.Calculate the MEAN difference and SD between traffic on these two Fridays at the 95% level;

Traffic Count

Dates6th (x1) 13th(x2)d = (x1 - x2)

1990,July139246138548

1990,July138012132908

1991,September 137055136018

1991,September 140675131843

1991,December 123552121641

1991,December 121139 120723

1992,March 128293125532

1992,March 124631 120249

1992,November 124609125770

1992,November 119584 116263

For the differences (all d's)the MEAN = _______ and the SD = __________

4)We can also do CONFIDENCE INTERVAL comparison of TWO population means that have the SAME NUMBER OF DATA VALUES (n1 = n2).Using the same traffic count data and statistics as above, the margin of error, E, formula isE = t-critical * s_d/sqrt(n)We will assume a significance level of = 5%(95% confidence level) with n=10 data points, hence df = (10 - 1 ) = 9, so t-critical = ______ ?What are the MEAN ______and SD _____for the "differences"?

E = _______ * _______ / ______= __________(fill in the different values and the calculated result).

Our Confidence Interval is(d-bar - E) < _d < (d-bar + E)= _________ < _d < __________

Conclusion:there is a 95% chance that this CI contains the true mean difference in traffic counts (for 10 dates).

(5)Is there a significant difference between these TWO population means regarding median incomes?Make sure to show your setup for the t-Test, df and how you found the t-Critical.Also, use software to find the p-value (probability) is it larger or smaller than ?Does this conclusion match the one based on the t-Test verses t-Critical?(It must).For the p-value, make sure you know which area (right or left) you need to use (greater than or less than).(If NOConfidence Level or is provided assume 95% and 5%, respectively)

Median Income for Males

$42,951$52,379 $42,544 $37,488 $49,281 $50,987 $60,705

$50,411 $66,760 $40,951 $43,902 $45,494 $41,528 $50,746

$45,183 $43,624 $43,993 $41,612 $46,313 $43,944 $56,708

$60,264 $50,053 $50,580 $40,202 $43,146 $41,635 $42,182

$41,803 $53,033 $60,568 $41,037 $50,388 $41,950 $44,660

Median Income for Females

$31,862$40,550 $36,048 $30,752 $41,817 $40,236 $47,476

$60,332 $33,823 $35,438 $37,242 $31,238 $39,150 $34,023

$33,269 $32,684 $31,844 $34,599 $48,748 $46,185 $36,931

$29,548 $33,865 $31,067 $33,424 $35,484 $41,021 $47,155

$42,113 $33,459 $32,462 $35,746 $31,274 $36,027 $37,089