Statistics

YOU MUST SHOW YOUR WORK. I need this by 11pm tonight.

1.       A math teacher believes that she has developed a review course that increases the scores of students on the math portion of the SAT exam. Based on reliable data, scores are normally distributed with a mean of 523 and standard deviation of 113. The teacher obtains a random of 1800 students, puts them through the review class, and finds that the mean SAT math score of the 1800 students is 526.

A.      State the null and alternative hypotheses

B.      Test the hypothesis at the α= 0.10 level of significance.

2.       Researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 11 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm³. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x̄= 8.49 and s=0.8. Conduct an appropriate test at the α= 0.01 level of significance.

3.       Previously, 21% of employed adults were satisfied with their chances for promotion. A manager wants to determine if this percentage has changed significantly since then. She randomly selects 260 employed adults and finds that 65 of them are completely satisfied with their chances for promotion. Is there sufficient evidence to conclude that the percentage of employed adults satisfied with their chances for promotion is significantly different from the previous percentage, at the α =0.1 level of significance?