Portage Learning Statistics Z-Test Study Guide Module 4 - Recently Updated Verified

Portage Learning Statistics Z-Test Study Guide Module 4 - Recently Updated Verified A frequency distribution that follows a bell-shaped, symmetrical, unimodal curve is known as the - answer - normal curve In a normal distribution, the mean is located in the - answer - middle of the curve In a normal distribution, what is the relationship between the mean, median, and mode? - answer - Mean~=Median~=Mode Mean = Median The further a value deviates from the mean, the ___ the frequency, thus scores beyond 2 stand deviations from the mean rarely occur in normal distribution - answer - the lower the frequency Data with __ frequencies are clustered around the mean - answer - the greatest A distribution with a smaller standard deviation has a curve with a ___ - answer - higher arc A distribution with a larger standard deviation has a curve with a __ - answer - lower arc A normal distribution can be defined by its - answer - mean and standard deviation The area under the curve represents the total relative frequency of a distribution and equals __ - answer - 100% In a normal curve, an equal number of distributions fall - answer - above and below the mean Normal distributions are approximated with the __ rule - answer - 68-95-99.7 About __ values fall within 1 SD of the mean About __ values fall within 2 SD of the mean About __ values fall within 3 SD of the mean - answer - 68-95-99.7 Calculate the 68-95-99.7 totals with a mean = 73 and standard deviation (sigma) = 4 - answer - 68% between 69-77 95% between 65-81 99.7% between 61-85 True/false: 68-95-99.7 rule only works when values are exactly 1, 2 or 3 standard deviations away from the mean. - answer - True In order to apply the concept of proportions to fractioned sigma values, the scores or values in the dataset must be standardized. A __ score is a score that is exactly observed - answer - raw value A __ score indicates exactly how many standard deviations a raw score is above or below the mean. - answer - z-score or standard score __ scores describe the exact location of a raw score within the whole distribution when compared to the mean. It converts each raw score, x, into a signed, numerical value. It describes how far a raw score is from the mean of the distribution. (x-σ) - answer - Z-scores The function of z-scores is - answer - to compare two scores when the standard deviation or the variance is known. It is useful for comparing 2 scores from different samples or populations. A positive z-score indicates - answer - a value above the mean A negative z-score indicates - answer - a value below the mean A z-score of 1.5 means that a raw score is __ standard deviations above the mean - answer - 1.5 z-score formula for a single raw score - answer - z= ((raw score) - (mean))/ (standard deviation) when calculating z-score for a single raw score, the ___ should be used. When calculating the z-score for a sample mean, the __ should be used. (denominator) - answer - Single raw: standard deviation σ Sample mean: standard error σx̄ (population standard deviation/sq root sample size n) z-score formula for sample mean - answer - z = (sample mean - population mean) / (standard deviation of sample /square root sample size) The __ table allows you to locate the proportion that corresponds to a z-score according to the __ rule - answer - standard normal, according to the 68-95-99.7 rule In a standard normal table, the decimal value listed for each z-score indicates the proportion of scores that lie ___ of that z-score in the distribution. - answer - to the left The proportion p = 0.00076 corresponds to z-3.17, written as: - answer - p(z-3.17) = 0.00076 The proportion p = 0.99924 corresponds to z-3.17, written as: - answer - p(z-3.17) = 0.99924 To find a proportion of values above the Z-score - answer - subtract the p-value from 1.00 To find a proportion of values that lies between two z-scores - answer - Find the proportion of the two z-sores and subtract the