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M650

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Statistics

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Jan 9, 2024

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M650 Question 1 Unbiased Sample 1. A sample that is representative of a population Standard Deviation 2. Value quantifying the spread about the mean of numeric values Standard Error 3. The standard deviation of a distribution of statistics resulting from sampling or an estimate of the standard deviation Random Sampling 4. A method of sampling where each member of the population is equally likely to be included in a sample Convenienc e Sampling 5. A method of sampling where easily accessible members of a population are sampled Sampling Error 6. The difference between observations in a sample and observations in the population Biased Sample 7. A sample obtained by a non-random sampling method Biased Statistic 8. The mean of a distribution of statistics is not equal to the parameter the statistic estimates Question 2 Sampling error can be eliminated by:  Increasing sample size  Obtaining an unbiased sample  Using a probability sampling method  Performing a census Question 3 Select all which are biased sampling methods  Survey two union workers for each non-union worker  Groups are selected by random sampling. People in the selected groups are surveyed.  Telephone survey  With each group composed of people with the same characteristic and each person belonging to only one group, a random sample is taken from each group.  Survey the first 20 people entering a particular coffee store on the last Tuesday before the next election Question 4 Simple Random 1. Each member of the population has an equal chance of being selected for a sample.

M650 Sampling Probabilit y Sampling Method 2. Each member of the population is assigned a unique number. Randomly select numbers from a list of assigned numbers. Systematic Random Sampling 3. Each member of the population is assigned a unique number. The first number is selected randomly. The remaining numbers are selected at equal intervals. Cluster Random Sampling 4. The population is divided into separate physical units. Each member of the population belongs to only one physical unit. Physical units are selected by simple random sampling. In each of the selected units, all the members are surveyed. Stratified Random Samplin 5. Each member belongs to only one unit of the same characteristic. A simple random sample of equal size is taken from each unit. Question 5 Statistical methods that assume the Normal probability distribution can be applied to processes whose data have a skew approximately < 1 or a histogram that is roughly bell shaped.  True  False Question 6 Select ALL true statements.  The standard normal probability distribution is applicable to the standardized value of a normal random variable = (value - mean)/sd, which is the number of standard deviations (sd) from the mean.  The mean of a standardized normally distributed random variable is 0 and the standard deviation is 1.  The Normal distribution is important because many processes are approximated by the Normal distribution, and many statistical procedures assume that the data are normally distributed.  The Normal probability distribution curve is bell shaped.  The mean the normal distribution is 0 and the standard deviation is 1 Question 7 STANDARDIZ E 1. Compute a Z-score from a value of a normal random variable, mean, and standard deviation. NORM.S.DIST 2. Compute the left-tail probability from a Z-score, and additional

M650 input 1 (0=height of curve, 1=area under curve). NORM.DIST 3. Compute the Z-score from a left-tail probability. NORM.INV 4. Compute the left-tail probability from a value of a normal random variable, mean, standard deviation, and additional input 1 (0=height of curve, 1=area under curve). NORM.S.INV 5. Compute the value of a normal random variable from a left-tail probability, mean, and standard deviation. Question 8 The probability distribution of the means of large samples taken from the same probability distribution will be approximately Normal regardless of the distribution the sample was taken from. This is called the  Law of Large Numbers  Law of Averages  Normal Distribution Theorem  Law of Large Sample Size  Central Limit Theorem Question 9 Select the true statements.  Distributions of sample means become approximately normally distributed when sample size is at least 30 for most populations.  Distributions of sample means are approximately normally distributed because the sample mean estimates the population mean.  Distributions of sample means become approximately normally distributed when sample size is at least 50 for highly skewed populations. Question 10 Sample Mean 1. Sample Standard Deviation 2.

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M650 Estimated Standard Error of Sample Means 3. Estimated Standard Error of Sample Proportions using sample proportion p as estimate of the population proportion 4. Question 11 According to the Empirical Rule what percent of the population is more than 1 standard deviation away from the mean?  99.7%  32%  5%  0.3%  68%  95% Question 12 According to the Empirical Rule what percent of the population is above 1 standard deviation above the mean, which is a right-tail probability?  97.35%  2.5%  81.5%  83.85%  16%  0.15% Question 13 What is the Z score where 50.0% of the normal distribution is below that z score and 50.0% of the normal distribution lies above that same z score?  1.64  1.28  2.33  0.39

M650  0.00  0.67 Question 14 The Z values of the limits of the area covering the middle 30.0% of the area under the normal curve are plus and minus  0.47  0.35  0.39  0.51  0.43  0.32 Question 15 If the mean annual return for common stocks is 11.5% and the standard deviation 13.5%, what is the probability that the stock returns are less than 10.5%?  40%  47%  0%  53%  15%  58% Question 16 The distribution of a product is unimodal and roughly symmetric. The package is labeled 12 oz. If the standard deviation is 0.2 ounces, what should the process mean be if 4% of the product is underweight?  14.38  15.35  11.38  12.35  10.41  13.41 Question 17

M650 If the mean annual return for a stock is 15%, what is the risk (standard deviation) you would take for a probability of 33% of a return being at least 21%?  11%  21%  6%  14%  8%  17% Question 18 The Chunkiest cookie factory changed their manufacturing process. The inspectors sampled 55 11.5-oz packages with mean 11.00 oz and a standard deviation of 1.5 oz. The CEO asks what is the lower weight boundary of the middle 55% of package weights.  13.16  9.87  14.69  8.82  10.64  11.69 Question 19 If the sample standard deviation is 7.15, what would be the estimated standard error of sample means for sample size 50? Write the result with 2 decimal places.  1.01 Question 20 The sample proportion is 0.50. What is the estimated standard error of the sampling distribution of sample proportions for sample of size 30?  0.0912

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