Exam 11: Hypothesis Tests Involving Two Sample Means

Women drivers In the past,young women drivers have maintained a better driving record than young men drivers.An insurance company is concerned with the driving record of its insured customers.Specifically,it conducts a test for the number of speeding tickets received during the past year by drivers between the ages of 18 and 25. Men Women =120 =85 =1.2 =0.4 =24.8 =10.6 -A test for the equality of average number of tickets per driver for the two groups is desired.Use $\alpha$ = 0.01.State the null and alternative hypothesis. H₀: ____________________ H₁: ____________________

Independent samples are those for which the selection process for one is not related to the selection process for the other.

The number of degrees of freedom associated with the unequal-variances t-test for comparing the means of two independent samples is n₁ + n₂ - 2.

Slacks Manufacturer A slacks manufacturer is deciding whether to purchase a new method for bonding seams together.Before purchasing a new method that bonds,or glues,the seams together,the manufacturer wishes to determine whether or not the "bonded" seams can withstand more pulling stress than standard seams sewn with thread.The creator of the new method provides a demonstration machine and supplies for the slacks maker to test.Two samples of the slacks produced are taken.Each pair of slacks has the seams tested in an application of force to determine the breaking point (in lbs.)for the seam.The sample results are: Sample 1: Sewn Sample 2: Glued =50 =50 =125. =165. =46. =57. -The test question is: At the 0.05 level of significance,is the gluing of seams better than sewing? What is the conclusion?

An important factor in choosing between the pooled-variances t-test and the unequal-variances t-test is whether we can assume the population means might be equal.

Slacks Manufacturer A slacks manufacturer is deciding whether to purchase a new method for bonding seams together.Before purchasing a new method that bonds,or glues,the seams together,the manufacturer wishes to determine whether or not the "bonded" seams can withstand more pulling stress than standard seams sewn with thread.The creator of the new method provides a demonstration machine and supplies for the slacks maker to test.Two samples of the slacks produced are taken.Each pair of slacks has the seams tested in an application of force to determine the breaking point (in lbs.)for the seam.The sample results are: Sample 1: Sewn Sample 2: Glued =50 =50 =125. =165. =46. =57. -The test question is: At the 0.05 level of significance,is the gluing of seams better than sewing? What is the decision rule?

Comparing the means or proportions from two independent samples requires comparing the calculated value of a test statistic with the computed p-value,then deciding whether the null hypothesis should be rejected.

National Management Assoc The National Management Association reports that during the past year,there has been a substantial increase in the use of "flextime" in the work place.Last year,a sample of 100 businesses was taken which indicated that 22% had implemented the use of "flextime." This year,a second survey of 100 showed that 29% were using flextime.At the 0.05 level,does this represent an increase in the proportion? -What is the value of the test statistic? Appropriate test: ____________________ Test statistic = ____________________

Which of the following statements are true?

Ford Motor Co. The Ford Motor Company,as part of its quality control program,began returning to the supplier all shipments of steel that had defects or faulty chemistry.When Ford began this program,the defective rate in 100 shipments was 9%.A recent survey indicated that 2.2% in 136 shipments was defective.Does this represent a significant improvement in the quality of the steel? Test at the 0.05 level. -State the null and alternative hypotheses. H₀:____________________ H₁: ____________________

An analyst is looking at two portfolios of common stocks in terms of the average price-earnings ratio.He wishes to determine if there is a difference between the two portfolios. Portfolio 1 Portfolio 2 =53 =50 =16.60 =17.62 =62.74 =127.95 Calculate a 99% confidence interval. ____________________ to ____________________

The number of degrees of freedom associated with a pooled-variance t-test is _________________________.

A sample of size 100 selected from one population has 60 successes,and a sample of size 150 selected from a second population has 95 successes.The test statistic for testing the equality of the population proportions equal to:

Realtor A new realtor in a large community is attempting to determine differences in the selling prices of houses in two sections of the community.Population 1 is the Northeast and Population 2 is the Southwest.The realtor is going to perform the hypothesis test: H₀: $\mu _ { 1 } = \mu _ { 2 }$ H₁: $\mu _ { 1 } \neq \mu _ { 2 }$ A random sample of 35 sale homes is taken from the Northeast and 41 from those in the Southwest using the multiple listing services.A Minitab summary of the results of the two samples expressed in thousands follows: N MEAN MEDIAN TRMEAN STDEV SE MEAN NORTHEAST 35 86.789 84.800 88.313 60.067 10.153 SOUTHWEST 41 60.490 62.200 61.857 14.740 2.302 -What is the decision rule at the 0.01 level of significance?

A typical example of dependent samples occurs when we have before-and-after measures of the same individuals.

SAT A new SAT preparation program claims that students will improve their verbal scores with a practice test after one month on the program.To validate their claim,they recorded the starting and practice verbal SAT scores of 12 individuals after a one-month period.The results are shown in the following table. Starting SAT Score Practice SAT Score 450 460 390 390 425 430 510 500 520 525 440 420 550 570 610 625 490 510 475 485 535 540 500 500 -State the null and alternative hypotheses.

Battery A new brand of battery for use in calculators and cameras is said to last significantly longer than another brand.A camera manufacturer is to test this brand (Y)with brand (X)to see if brand Y has a longer life.If brand Y does last longer,the camera manufacturer will equip their new cameras with them.If not,they will equip them with brand X that is less costly.Twenty cameras are equipped as follows: ten with brand Y batteries and ten with brand X batteries and the life of the batteries measured.Is brand Y superior (does it last longer)to brand X? To answer this question,the camera manufacturer uses a 0.01 significance level and knows that the populations are normally distributed with equal variances.Sample data are: Brand Brand =10 =10 =500 hours =650 hours =400 =484 -State the null and alternative hypotheses. H₀: ____________________ H₁: ____________________

When the necessary conditions are met,a two-tail test is being conducted to test the difference between two population proportions.If the value of the test statistic z is 2.05,then the p-value is:

Real pop A marketing research firm is conducting a survey to determine if there is a difference in consumer choice in the selection of two rival soft drinks.Those surveyed were asked to rank the taste from 1-10 with 10 being the highest rating.A summary of the survey follows: Real Cola New Pep =30 =36 =7.5 =5.4 =10.6 =14.9 -What is the conclusion?

Realtor A new realtor in a large community is attempting to determine differences in the selling prices of houses in two sections of the community.Population 1 is the Northeast and Population 2 is the Southwest.The realtor is going to perform the hypothesis test: H₀: $\mu _ { 1 } = \mu _ { 2 }$ H₁: $\mu _ { 1 } \neq \mu _ { 2 }$ A random sample of 35 sale homes is taken from the Northeast and 41 from those in the Southwest using the multiple listing services.A Minitab summary of the results of the two samples expressed in thousands follows: N MEAN MEDIAN TRMEAN STDEV SE MEAN NORTHEAST 35 86.789 84.800 88.313 60.067 10.153 SOUTHWEST 41 60.490 62.200 61.857 14.740 2.302 -What is the standard error of the difference between the two means?