Statistics: Confidence Intervals and Hypothesis Testing, Exercises of Applied Statistics

Download Statistics: Confidence Intervals and Hypothesis Testing and more Exercises Applied Statistics in PDF only on Docsity! Hypothesis tests: Test Null Hypothesis Test Statistic One-sample z-test for means M=Up z= — Nn One-sample t-test for means M=U, t=i THe: df= Matched Pairs t-test Mp =Hp 1-42 feat . sin One-sample z-test for proportions P=D, z=—_PoP pl—p) n Two-sample t-test for means Uy —My =0 OF fh = py t= im ; df=min(aln2)-1 Si 2 + m My Two-sample z-test for proportion p, — p) =0 or p, = p» AC Goodness of fit test no change Confidence Intervals General formula: statistic+ margin of error An 80% confidence interval was calculated to show the difference in passing percentages of the Biology Final Exam and Algebra Final Exam. The resulting interval was [.04, .12]. Answer the following, if it is possible to calculate: • The difference in the sample proportions. • The pass rate of the Algebra Final Exam. • The margin of error for the difference between these passrates. • Are the two samples of equal size? • Was a t-test or a z-test used? • Which final exam had the higher passrate? A SRS of 81 observations produced a mean of 250 with a standard deviation of 22. Determine the 95% confidence interval for the population mean. A random sample of 64 observations produced a sample proportion of 0.23. Determine the 95% confidence interval for the population proportion. After performing a p-test, the P-Value is found to be smaller than the significance level (α). How should you proceed? a. Reject the Null Hypothesis b. Accept the Alternate Hypothesis c. Fail to Reject the Null Hypothesis d. Accept the Null Hypothesis e. Fail to Reject the Alternate Hypothesis f. Perform a q-test to confirm results g. Accept them both, the more the merrier! h. Throw a party i. Any or All of the above are acceptable (no one really hypothesis tests anyway) A one-sample z-statistic for a test of Ho: μ = 53, and Ha: μ > 53 based of 75 observations and calculations show z = 1.837. Determine the p-value. An assortment of candies claims that their sample bag contains the following: 15% Snickers, 35% Milky Way, 25% Three Musketeers, 15% Almond Joy and 10% Mounds. From a bag of 200 candies, you find there are 30 Snickers, 35 Milky Way, 40 Three Musketeers, 45 Almond Joy and 50 Mounds. Use a χ2 test for goodness of fit to determine if the company’s claim is accurate. (Use α = 0.01) Continued from Previous Slide Snickers 15% 30 Milky Way 35% 35 Three Musketeers 25% 40 Almond Joy 15% 45 Mounds 10% 50 Total 200 To determine the effectiveness of a summer reading program, a sample of 50 children were tested for their reading speed before and after the program. The mean difference of this sample was an increased reading speed of 1.4 minutes for one page of text (with a standard deviation of 0.03 minutes). Determine if the reading program was effective of the program with a significance of 2%. Calculate the Test Statistic. To determine the effectiveness of a summer reading program, a sample of 50 children were tested for their reading speed before and after the program. The mean difference of this sample was an increased reading speed of 1.4 minutes for one page of text (with a standard deviation of 0.03 minutes). Determine if the reading program was effective of the program with a significance of 2%. Determine the p-value. To determine the effectiveness of a summer reading program, a sample of 50 children were tested for their reading speed before and after the program. The mean difference of this sample was an increased reading speed of 1.4 minutes for one page of text (with a standard deviation of 0.03 minutes). Determine if the reading program was effective of the program with a significance of 2%. Draw a conclusion. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance. Calculate your test statistic. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance. Determine your p-value. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance. Draw a conclusion. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of 0.2. Test, with a significance of 5%, if there is doubt in the accepted mean. Calculate your test statistic. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of 0.2. Test, with a significance of 5%, if there is doubt in the accepted mean. Determine your p-value. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of 0.2. Test, with a significance of 5%, if there is doubt in the accepted mean. Draw a conclusion.