# Penn State STAT 200 Assignment

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# 1. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.

c. If the problem is a hypothesis test, indicated if it has a lower-tail, upper-tail, or two-tail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.

Unless indicated otherwise, you DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc. Just type your answer to a., b., and c. above in the space below.

Problem: A large organization is being investigated to determine if its recruitment is sex-biased. Tables 1 and 2, respectively, show the classification of applicants for sales and for secretarial positions according to gender and result of interview. Table 3 is an aggregation of the corresponding entries of Table 1 and Table 2. Answer each of the following:

i. According to the data in tables 1 and 2, does there seem to be an association with gender and hiring status at the 5% significance level?

ii. Does the data in Table 3 indicate the same result?

Table 1 Sales Positions

 Offered Denied Total Male 25 50 75 Female 75 150 225 Total 100 200 300

Table 2 Secretarial Positions

 Offered Denied Total Male 150 50 200 Female 75 25 100 Total 225 75 300

Table 3 Secretarial and Sales Positions

 Offered Denied Total Male 175 100 275 Female 150 175 325 Total 325 275 600

# 2. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.

c. If the problem is a hypothesis test, indicated if it has a lower-tail, upper-tail, or two-tail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.

You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.

Problem: An instructor at Arizona State University asked a random sample of 8 students to record their study times in a elementary statistics course. She then made a table for total hours studied over 2 weeks and test scores at the end of the 2 weeks. Here are the data:

Study time  10   15   12   20    8     16    14   22

Test Scores  92   75   86   76   92   80   84    81

Assuming that a linear association exists, how are the data correlated? Determine the exact linear relationship between study time and test scores and use it to estimate the predicted test score for a student who studies 12 hours.

# 3. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.

c. If the problem is a hypothesis test, indicated if it has a lower-tail, upper-tail, or two-tail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.

You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.

Problem: A company sells a strong commercial floor cleaner and claims that the flashpoint (the lowest temperature at which the vapor of a combustible liquid can be ignited in air) exceeds 200ºF. A random sample of cleaner was obtained and the flashpoint of each was measured. The sample mean was 198.2ºF and the sample standard deviation was 10ºF. At the 1% significance level, is there sufficient evidence to support the companies claim?

# 4. Directions: Read the following problem. In your answer, please include the following information:

a. Determine if the problem is either a test of hypothesis, a confidence interval or something else and specify the ‘key words’ found in the problem that demonstrate your choice.

b. Determine the procedure name and parameters involved for each problem (use the Stat 200 Formulas and Techniques Summary document.) Specify the ‘key words’ found in the problem that lead you to this choice.

c. If the problem is a hypothesis test, indicated if it has a lower-tail, upper-tail, or two-tail alternative hypothesis as well as the test statistic formula for the test. If the problem is a confidence interval then indicate the formula used for the margin of error.

You DO NOT need to do the ACTUAL test of hypothesis, confidence interval, etc., just answer parts a, b, and c for the problem.

Summary Table for Statistical Techniques

 Inference Parameter Statistic Type ofData Examples Analysis MinitabCommand Conditions 1 Estimating amean Onepopulationmean µ sample mean numerical What is the averageweight of adults?What is the averagecholesterol level ofadult females? 1-sample t-interval Stat>Basicstatistics>1-sample t data approximately normalorhave a large samplesize (n ≥ 30) 2 Test about amean Onepopulationmean µ sample mean numerical Is the average GPAof juniors at PennState higher than3.0?Is the averageWinter temperaturein State Collegeless than 42ْ F? Ho : µ = µoHa : µ ¹ µoor Ha: µ > µoor Ha : µ < µoThe one sample t test: Stat>Basicstatistics>1-sample t data approximately normalorhave a large samplesize (n ≥ 30) 3 Estimating aproportion Onepopulationproportionp sampleproportion categorical(binary) What is theproportion of malesin the world?What is theproportion ofstudents that smoke? 1-proportion Z-interval Stat>Basicstatistics>1-sampleproportion n≥ 10 and n (1-) ≥ 10 4 Test about aproportion Onepopulationproportionp sampleproportion categorical(binary) Is the proportionof females differentfrom 0.5?Is the proportion ofstudents who failStat200 less than0.1? Ho : p = poHa : p ¹ poor Ha: p > poor Ha : p < poThe one proportion Z-test: Stat>Basicstatistics>1-sampleproportion n po ³ 10andn (1-po ) ³ 10 Inference Parameter Statistic Type ofData Examples Analysis MinitabCommand Conditions 5 Estimating thedifference oftwo means difference intwopopulationmeansµ1-µ2 difference intwo samplemeans numerical How different arethe mean GPAs ofmales and females?How many fewercolds do vitamin Ctakers get, onaverage, than nonvitamin C takers? two-sample t-interval  See text, page 445, forthe s.e. of the difference Stat>Basicstatistics>2-sample t independent samples fromthe two populationsdata in each sample areabout normal or largesamples (ni ≥ 30) 6 Test tocompare twomeans difference intwopopulationmeansµ1-µ2 difference intwo samplemeans numerical Do the mean pulserates of exercisersand non-exercisersdiffer?Is the mean EDSscore for dropoutsgreater than themean EDS score forgraduates? Ho : µ1 = µ2Ha : µ1 ¹ µ2or Ha : µ1 > µ2or Ha : µ1 < µ2The two sample t test:See text, page 445, forthe s.e. of the difference Stat>Basicstatistics>2-sample t independent samples fromthe two populationsdata in each sample areabout normal or largesamples (ni ≥ 30) 7 Estimating amean withpaired data mean ofpaireddifferenceµD sample meanofdifference numerical What is thedifferencein pulse rates, on theaverage, before andafter exercise? paired t-interval Stat>Basicstatistics>Paired t differences approximatelynormalorhave a large numberof pairs (n ≥ 30) 8 Test about amean withpaired data mean ofpaireddifferenceµD sample meanofdifference numerical Is the difference inIQ of pairs of twinszero?Are the pulse ratesof people higherafter exercise? Ho : µD = 0Ha : µD ¹ 0or Ha: µD > 0or Ha : µD < 0 Stat>Basicstatistics>Paired t differences approximatelynormalorhave a large numberof pairs (n ≥ 30)

 Inference Parameter Statistic Type ofData Examples Analysis MinitabCommand Conditions 9 Estimating thedifference oftwoproportions difference intwopopulationproportionsp1-p2 difference intwo sampleproportions categorical(binary) How different arethe percentages ofmale and femalesmokers?How different arethe percentages ofupper- and lower-class bingedrinkers? two-proportions Z-interval  See notes for s.e. formula Stat>Basicstatistics>2 proportions independent samplesfrom the two populationsn≥ 10 and (1-n)≥ 10for each sample 10 Test tocompare twoproportions difference intwopopulationproportionsp1-p2 difference intwo sampleproportions categorical(binary) Is the percentage ofmales with lungcancer higherthan the percentageof females with lungcancer?Are the percentagesof upper- and lower-class binge drinkersdifferent? Ho : p1 = p2Ha : p1 ¹ p2or Ha : p1 > p2or Ha : p1 < p2The two proportion z test: See notes for s.e. formula Stat>Basicstatistics>2 proportions independent samplesfrom the two populationsn≥ 10 and (1-n)≥ 10for each sample 11 Relationshipin a 2-waytable relationshipbetween twocategoricalvariablesordifference intwo or morepopulationproportions the observedcounts in atwo-way table categorical Is there arelationshipbetween smokingand lung cancer?Do the proportionsof students in eachclass who smokediffer? Ho : The two variables arenot relatedHa : The two variables arerelatedThe chi-square statistic: Stat>Tables>CrossTabu-lation >Chi-Square analysis forFor summarizedData: Stat>Tables> Chi-Square. all expected counts shouldbe greater than 1at least 80% of the cellsshould have an expectedcount greater than 5

 Inference Parameter Statistic Type ofData Examples Analysis MinitabCommand Conditions 12 Test about aslope slope of thepopulationregressionline b1 sampleestimate ofthe slopeb1 numerical Is there a linearrelationship betweenheight and weight ofa person? Ho : b1 = 0Ha : b1 ¹ 0or Ha : b1 > 0or Ha : b1 < 0The t test with n-2 degrees offreedom: Stat>Regression>Regression the form of the equationthat links the two variablesmust be correctthe error terms are normallydistributedthe errors terms haveequal variancesthe error terms areindependent of each other 13 Test tocompareseveralmeans Populationmeans of thek populationsµ1,µ2,….., ,µk Sample meansof the kpopulationsx1,x2,….., ,xk numerical Is there a differencebetween the meanGPA of Freshman,Sophomore, Juniorand Senior classes? Ho : µ1=µ2=˙˙˙ =µkHa : not all the means areequalThe F test for one-wayANOVA: Stat>ANOVA>Oneway each population is normallydistributedindependent samples fromthe k populationsequal population standarddeviations

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