SOLUTION: The mean SAT score in mathematics, μ, is 53. The standard deviation of these scores is 41. A special preparation course claims that its graduates will score higher, on average
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Question 897168: The mean SAT score in mathematics, μ, is 53. The standard deviation of these scores is 41. A special preparation course claims that its graduates will score higher, on average, than the mean score 503. A random sample of 70 students completed the course, and their mean SAT score in mathematics was 505. 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 is also 41.
A.) Null Hypothesis:
B.) Alternative Hypothesis:
C.) The Value of the test statistic:
D.) The P-Value:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The mean SAT score in mathematics, μ, is 503. The standard deviation of these scores is 41.
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A special preparation course claims that its graduates will score higher, on average, than the mean score 503.
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A random sample of 70 students completed the course, and their mean SAT score in mathematics was 505.
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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 is also 41.
A.) Null Hypothesis:
Ho: u = 503
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B.) Alternative Hypothesis:
Ha: u > 503 (claim)
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C.) The Value of the test statistic:
z(505) = (505-503)/[41/sqrt(70)] = 2/4.9 = 0.4081
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D.) The P-Value = P(z > 0.4081) = normalcdf(0.4081,100) = 0.34
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Cheers,
Stan H.
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