The mean SAT score in mathematics, µ, is 502. The standard deviation of these scores is 46. A special preparation course claims that its graduates will score higher, on average, than the mean score 502. A random sample of 30 students completed the course, and their mean SAT score in mathematics was 506. Assume that the population is normally distributed. At the 0.05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates in also 46. Perform a one-tailed. Then fill in the table below Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0 : ____ The alternative hypothesis: H1: _____ The type of test statistic: (choose one) ____ The value of the test statistic: ____ (Round to at least three decimal places.) The p-value: _______ (Round to at least three decimal places) Can we support the preparation course’s claim that its graduates score higher in SAT? YES ___ NO _____

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...