A Hypothesis Testing Situation Is Given $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 472 \\ \mathrm { H } _ { \mathrm { a } } : \mu \neq 472 . \end{array}$$

question 53

Essay

A hypothesis testing situation is given. The population standard deviation, sample size, and significance level are given.Complete the table to give the probability of a Type II error and the power for each of the given values of µ. Use the table to draw the power curve.
-In 1990, the average math SAT score for students at one school was 472. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 1990 mean of 472. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 472 \\ \mathrm { H } _ { \mathrm { a } } : \mu \neq 472 . \end{array}$$ Assume that $\sigma = 74 , \mathrm { n } = 54$ , and the significance level is $0.01$ . Find the probability of a Type II error and the power for $\mu = 424,430,440,450,460,470,474,484,494,504,514,520$ . 430 440 450 460 470 474 484 494 504 514 520

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Definitions:

Townshend Duties

A series of British Acts passed in 1767 imposing taxes on the American colonies on goods such as tea, paper, and glass, leading to widespread protest.

Nonimportation Associations

Groups formed by American colonists before the American Revolution to boycott goods imported from Britain, aiming to put economic pressure on Britain to repeal unpopular legislation.