1. An engineer wants to measure the bias in a pH meter. She uses the meter to measure the pH in 6 neutral substances and obtains pH readings of 7.01, 7.04, 6.97, 6.99, 7.04, and 7.07 (6 pts) a. Find the mean and standard deviation for the pH values (show your work). b. Create a 95% confidence interval for the pH values read by this meter. c. Explain in context what your confidence interval tells you about the pH values read by this meter. d. The actual pH of the substances tested was 7. Does it seem there is evidence the pH meter is testing inaccurately? 2. In a study, researchers wanted to measure the effect of alcohol ion the development of the hippocampal region in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders to compare the hippocampal volumes in the alcoholic adolescents to the normal volume of 9.02 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume was distributed normally with a mean of 8.10 cm 3 and a standard deviation of 1.67 cm3. (5 pts) a. The researchers wanted to determine if the hippocampal values in the alcoholic adolescents were different from the normal volume of 9.02 cm 3. Write the null and alternative hypotheses for this question. b. What are the assumptions (conditions) of this test? Are the assumptions met for this sample? c. Perform the appropriate test including the formula that you used, the calculated value of the t-statistic, and the t-critical you compared your t-statistic to using a significance level of .05. Then, state your conclusion to the test. d. No supposed the researchers wanted to determine specifically if the hippocampal values in the alcoholic adolescents were less than the normal volume of 9.02 cm 3. Rewrite your null and alternative hypothesis, then repeat the test and state your conclusion. 3. A set of researchers believed that the normal body temperature of children is actually more than 98.6 degrees. They measured the temperature in 14 randomly selected healthy adolescents and found a sample mean of 98.9 with a standard deviation of 0.7 degrees with the temperatures being normally distributed. (5 pts) a. Write the null and alternate hypothesis. b. Calculate the test statistic and write a conclusion for this question. c. Now suppose a sample of 125 adolescents was taken and the same mean (98.9) and standard deviation (.7) was achieved. Repeat the test. d. Explain what caused the difference between the outcomes for parts b and c. Copyright 2017 Department of Statistics and Data Sciences. All rights reserved