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 _____
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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 _____
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