report three things for this distribution of sample means: its shape, its expected value, and its standard error.
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Imagine a distribution of sample means for samples of n = 25 selected from a population with a
Let , X→N(μ=25 , σ=5) , n=25
Our aim is to report three things for this distribution of sample means: its shape, its expected value, and its standard error.
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- This is for statistics and probabilityFor data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is p = 1 - 7.2 where p is the minimum percentage of scores that fall within k standard deviations on both sides of the mean. Use this formula to answer the following questions. a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 2.1 standard deviations on both sides of the mean? b) If you have scores that are normally distributed, find the percentage of scores that fall within 2.1 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 96 percent of the scores? Note: To answer part c you will need to solve the equation for k.An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 8 IQ points of the true mean. Assume that σ=10 and determine the required sample size.
- In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information. 0.235 0.245 0.286 0.263 0.268 0.339 0.299 1.3 3.4 5.5 3.8 3.5 7.3 5.0 A USE SALT (a) Make a scatter diagram of the data. Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill No Solution 2 OHelp 123 0.24 0.25 026 027 028 029 0.3 031 0.32 0.33 WebAssign. Graphing Tool (b) Use a calculator to verify that Ex = 1.935, Ex² = 0.542, Ey = 29.8, Ey2 = 148.48 and Exy = 8.619. Compute r. (Round your answer to four decimal places.) As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer. O Given our value of r, y should tend to decrease as x…See pictures for question D and E and (A, B and Cand was submitted on a different question. According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 44 months. A researcher for a consumer advocate group tests this by selecting 16 bulbs at random. For the bulbs in the sample, the mean lifetime is 47 months. It is known that the population standard deviation of the lifetimes is 5 months. Assume that the population is normally distributed. Can we conclude, at the 0.10 level of significance, that the population mean lifetime, μ, of light bulbs made by this manufacturer differs from 44 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below.The mean age of graduate students at a University is at most 31 years with a standard deviation of 2 years. A random sample of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is 3 years. Are the data significant at the 1% level? a. State the null and alternative hypothesesb. Performzscore and find p-valuec. Perform Cohen's d equationd. State answer
- Use the formula to find the standard error of the distribution of differences in sample means, I1 – X2. Samples of size 110 from Population 1 with mean 82 and standard deviation 14 and samples of size 80 from Population 2 with mean 76 and standard deviation 17 Round your answer for the standard error to two decimal places. standard error = iA variable of two populations has a mean of 30 and a standard deviation of 18 for one of the populations and a mean of 30 and a standard deviation of 32 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 16, respectively, find the mean and standard deviation of X₁ -X₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁-X₂ is (Round to four decimal places as needed.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. OA. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x₁-x₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. B. No, the formulas for the mean and standard deviation of…The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.95 ounces and a standard deviation of 0.2 ounces. Suppose that you draw a random sample of 42 cans. Parti) Suppose the number of cans drawn is doubled. How will the standard deviation sample mean weight change? A. It will decrease by a factor of √2. B. It will increase by a factor of √2. C. It will increase by a factor of 2. D. It will decrease by a factor of 2. E. It will remain unchanged. Part ii) Suppose the number of cans drawn is doubled. How will the mean of the sample mean weight change? ▸ A. It will increase by a factor of √2. B. It will decrease by a factor of 2. C. It will increase by a factor of 2. D. It will decrease by a factor of √2. E. It will remain unchanged. Part iii) Consider the statement: The distribution of the mean weight of the sampled cans of Ocean brand tuna is Normal." A. It…
- Use the data in the Excel workbook, on the worksheet labeled "Sample," for this question. The first column is just an observation index labeled i to name each observation. The observations are a simple random sample with replacement from a much larger population. The second column contains specific values y of a random variable Y found in some sampled population. The population standard deviation is not known to you, but it is known that Y has a Normal distribution in the sampled population. Compute the lower bound of an 85% confidence interval for the population mean of the random variable Y. i y 1 37 2 40 3 31 4 27 5 23 6 33 7 29 8 26 9 39 10 28 11 34 12 39 13 31 14 34 15 39 16 33 17 31 18 42Suppose baby kittens' weights are normally distributed with a mean of 11.4 and a standard deviation of 2.1. The Z-score tells you how many units above the average (if Z-score is positive) or below the average (if Z- Score is negative) any particular baby kitten's weight is. Find the baby kitten weight that corresponds to the following Z-scores. Use the formula Z where u is the mean, o is the standard deviation, and X is the baby kitten weight. a. Z = = 0.07, X = b. Z = 1.63, X =The temperature distribution of city D has a population mean µ= 21.3, and standard deviation o = 4.8. You randomly select 12 days and get the temperature for these days. Then you compute the sample mean. What is the maximum sample mean value in the bottom 0.22 x 100% of the sample mean distribution? Note that we're talking about the distribution of the sampling mean. Give your answer to 2 decimal places.
