Perform the following hypothesis test using the P-value method . Be sure to stat

Question

Perform the following hypothesis test using the P-value method. Be sure to state the null and alternative hypotheses, calculate the test statistic, find the P-value, compare the P-value to teh level of significance, and state the conclusion. Use English if you cannot write the mathematical symbols.

Suppose a high school principal claims that the mean SAT score in math at his school is better than 550. A random sample of 72 students has a mean score of 574. Assume that the population standard deviation is 100. Is the principal's claim valid at the .10 level?

Explanation / Answer

As p-value is less than the significance level, we reject the null hypothesis.

There are significant evidence to conclude that mean SAT score in math at the school is better than 550

Below are the null and alternate hypothesis H0: mu = 550 Ha: mu > 550 This is right tailed z - test Critical value of test statistic is 1.2816 Here, n = 72 , xbar = 574 , mu = 550 and s = 100 Test statistic, z = (xbar - mu)/(s/sqrt(n)) z = (574 - 550)/(100/(sqrt(72)) z = 2.0365 p-value = 0.0209

As p-value is less than the significance level, we reject the null hypothesis.

There are significant evidence to conclude that mean SAT score in math at the school is better than 550

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