Test Statistic / Z-Test vs. T-Test Question?
Since we are testing for proportion, a z-test is OK. Also, we have a large sample. a) H0: Median income in 2003 is $52,000 ( p=0.5) HA: Median income is over $52,000 (p > 0.5) p = proportion of people with income over $52,000 in 2003 b) Sample proportion phat = 0.56 Variance of proportion = p*(1-p)/n = 0.5(0.5)/750 =0.0003333 S.D. of p is sqrt[0.000333] = 0.0183 Z = ( 0.56 - 0.5 ) / 0.0183 = 3.2863 c) P( z > 3.29) = 0.00001 The critical z assuming a 5 % level of significance is 1.645. 3.29 > 1.645; hence, reject H0 and accept HA. The proportion of people with median income $52,000 is greater than 50 %. Note: We need to know in 1999, what percentage of people had income over $52,000 to precisely do a statistical test. (or at least a sample estimate taken in 1999).
Statistical Analysis help?
I'm having trouble trying to understand this question.. can someone help me? A golf club manufacturer claims that the median length of a drive using its driver is 250 yards. A consumer group disputes the claim, indicating that the median will be considerably less. A sample of 500 drives is measured; of these 220 were above 250 yards, and none was exactly 250 yards. The null and alternate hypotheses are:
Do you often refer to statistics (median, std. deviation, data confidence) in your usability tests - mainly online (with big number of participants)?
Michael,We are just started to mature the quantitative side of our practice. The journey began 1.5 years ago after completing Jeff Sauros (http://wwww.measuingusability.com) Practical Stats for User Research and then acquiring a remote usability testing tool. The studies we've completed so far focused on time on task but we've also using the statistical techniques to analyze production data for A/B tests.
Math help. TEN POINTS!! ~ Statistics [Mean,Median and Mode]?
1. The mean of the following data is 37.625: 3.0.1.7.8.11.31,15,99,98,92,81,85,87,5... If the data value is multiplied by 2 and increased by 5, what is the mean of the transformed data set? 2. Sid received grades of 92,84,70 on three test. Find his test average. 3. Lizzy had grades of 90,90,92 and 78 on four english test. What grade must she obtain on her next test so the avredge for the 5 test will be 90 ? 4. For the first 6 days of the week, the average rainfall in Chicago is 1.2 inches. On the last day of the week, 1.9 inches of rain fell. What is the average rainfall for the week ? 5. The weekly salary of six employees in a small firm are $440, $445, $445, $450, $450 and $620. (a) For these six salaries find the mean, mediam and mode. (b) If negotiations for new salaries are in session and you represent managment, which measure of central tendancy will you use as the average salary? Explain your answer. (c) If negotiations are in session and you represent the labor union, which measure of central tendancy will you use as an average salary? Explain your answer.
AP statistics AP statistics?
Last year a small accounting firm paid each of its five clerks $22000, two Junior accountants $50000 each, and the firm's owner $270000. what is the mean salary paid at this firm? how many of the employees earn less than the mean? what is the median salary? write a sentence to describe how an unethical recruiter could use statistics to mislead prospective employees.
How do I perform statistical tests on test statistics?
So, if you've a dataset of descriptive statistics (averages, range, mode, median, etc.) and you want to perform statistical tests on it then first thing you need to see what type of distribution they follow. If you’re not sure then you can quickly use Tukey’s Quick Test (for averages). But, Tukey’s test has some conditions to follow before using them, such asSample sizes should be roughly sameSamples should be independent of each otherOutliers should be avoidedHowever, if you’re sure that it’s a normally distributed data, then just go for t-tests of ANOVA. Determine how many descriptive statistics you want to compare (One? Two? Three or more?) and use 1 Sample-t-test or 2-Sample-t-test or ANOVA, or Paired t-test according to your requirement.If you realize that data is not normally distributed, then try to find out what distribution they follow logically. Is it Weibull? Left or right skewed? or something else? If you’re not sure then jut transform your dataset using Box-Cox transformation and figure out the lambada value which would fit the data.That’s just for Averages though. If you want to test for medians, then routemap is same as average. 1) Find out distribution 2) Normal? 3) Yes: same as average tests. No: Go for Sign test, Mood’s median test, Kruskal-Wallis, etc. Similar test are for ranges as well.Anyway, point is, each of these test has their own conditions before you can apply them. Key is determining: Can I use this test? Using the test is simple, but determining if the test would be valid for our dataset or not, is difficult. Minitab, a statistical tool, has some good tools which would help in these tests.
AP Statistics Help?
The sample medians and means for the two groups were slightly different. -- This is okay for using the student t, testing this difference is the point of the t-test The distribution of the data was moderately skewed. -- this is okay for using the student t, it is very unlikely the data collected would be perfectly symmetric. The data are integers between 1 and 10 and so cannot be normal. -- if the data is not normal then the student t cannot be used. remember that the student t is an approximation of the standard normal such that the error in using the sample variance as an estimator of the populaiton standard deviation is accounted for. Only the most severe departures from normality. -- again this is okay. outliers and small samples are subject to this. However you must use caution here. if you cannot identify the data points as outliers then it is evidence that the data does not follow a normal distribution. The t procedure can always be used. -- No.
Statistics help please?
1.The durations of a random sample of 16 commercials are below (in seconds). Find the mean, median, and mode of these durations. 30, 12, 26, 7, 14, 35, 20, 30, 55, 8, 35, 18, 42, 15, 30, 10 a. Mean = 24.19, median = 30, mode = 23 b. Mean = 20.13, median = 21, mode = 35 c. Mean = 24.19, median = 23, mode = 30 d. Mean = 20, median = 24.19, mode = 30 2.A random sample of 9 catfish from Lake Marion gave the following weights rounded to the nearest pound: 3, 4, 11, 6, 5, 7, 6, 2, 4 Find the range. a. 4 b. 5 c. 7 d. 9 3.Using the information from question #2, find the sample mean for the data. a. 5.33 b. 9 c. 7 d. 2.65 4.Using the information from problem #2, find the sample variance (use your calculator). a. 2.65 b. 5 c. 7 d. 5.33 5.Using the data from problem #2, find the sample standard deviation (use your calculator) a. 5.33 b. 2.65 c. 2.49 d. 7 6.A random sample of 30 receipts for individuals shopping at the Community DrugStore showed the sample mean to be x-bar = $28.19 with a sample standard deviation of s = $4.06. Compute the coefficient of variation for this data. a. 6.94% b. 14.4% c. 694% d. 4.32% 7.Use the information from problem #6 and Use Chebyshev’s Theorem to find the smallest interval centered on the mean in which we can expect at least 88.9% of the data to fall. a. 16.01 to 40.37 b. 24.13 to 28.19 c. 20.07 to 36.31 d. 11.95 to 44.43 8.What are the numbers used in making a box-and-whisker plot? a. Low value, Q1, median, Q3, high value b. s, mean, s2, interquartile range c. Low value, interquartile range, high value d. Low Value, Q1, mean, Q3, high value 9.Luke took a test and scored in the 88th percentile. What percentage of the scores were above his score? a. 87% b. 13% c. 12% d. 88% 10.Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were: 73, 74, 63, 64, 80, 72, 64, 64, 68, 75, 65, 65, 71, 72, 74, 50, 65, 68, 69, 66, 67, 67, 66 Are there any data values that may be suspected outliers? a. 61.5 b. 71.5 c. 80 d. 50