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Martin, Physicist

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1. calculate the sample size for a hypothesis test that will

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1. calculate the sample size for a hypothesis test that will be required to detect an increase of 0.5σ from the mean of one population at α = 0.05 and β = 0.05? (Note: The population standard deviation is known use µ for the mean) (10 points)

2. The ACT exam has composite scores ranging from 1 to 36. It is generally thought that the mean composite score for the ACT is 20 points but it may have increased in the last years. SHOW ALL WORK PLZ

a)Write the null and alternative hypotheses.

b)Given n = 36, level of significance = 0.05, and Sigma= 5, Draw a normal curve and label “acceptance” and “rejection” regions. Find the value of x-bar that would cause us to reject the null hypothesis.

c)Draw the normal curves, label α and β regions, and hand-calculate the probability of a committing a Type II error, β, if the true population mean score is 21.2.

3. People were waiting in line to see a new movie. The following is the order in which males and females were in line. SHOW ALL WORK PLZ

F F M M M M M M F F F F M M M F F F F F M M M M M F F M M M

Test the sequence for randomness at the 0.05 level of significance.

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