Problems (16 pL 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 of7.13, 7.04, 7.07, 6.99, 7.10, and 7.17 (6 pts) a. Find the mean and standard deviation for the pH values (show your work). {2 pts) s. Create a 95% condence interval for the pH values read by this meter. Use at critical value of 2.571. (2 pts) c. Explain in context what your condence interval tells you about the pH values read by this meter. (1 pt) a. The actual pH of the substances tested was 6.6. Is there evidence the pH meter is testing inaccurately? (1 pt) 2. In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The researchers randomly selected 40 adolescents with alcohol use disorders to compare the hippocampal volumes in the alcoholic adolescents to the normal volume of 9.12 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume was distributed normally with a mean of 8.35 cm3 and a standard deviation of 1.65 em3' (5 pts) a. The researchers wanted to determine if the hippocampal values in the alcoholic adolescents were different from the normal volume of 9'. 12 cm]. Write the null and alternative hypotheses for this question. Use at critical value of 2.023. (- 5pm) 1:. What are the assumptions (conditions) of this test? Are the assumptions met for this sample? (1th 1:. Perform the appropriate test including the formula that you used, the calculated value of the tstatistic, and the tcritical you compared your t-statistic to using a signicance level of .05. Then. state your conclusion to the test. (2 pts) a Calculate and interpret the 95% confidence interval for the test. Use a t critical of2.023. (1.5 pts). 1A set of researchers believed that the normal body temperature of children is actually different than 97.52 degrees while sleeping. They measured the temperature in 23 randomly selected healthy adolescents and found a sample mean of 97.8 degrees with a standard deviation of 0.91 degrees with the temperatures being normally distributed. Use a t critical value of 2.07 (5 pts). a. Write the null and alternate hypothesis. (.5 pts) 1:. Calculate the test statistic and write a conclusion for this question. (2.5 pts) c. Now suppose a sample of 180 adolescents was taken and the same mean (97.8) and standard deviation (.91) was achieved. Repeat the test and write a nevi.r conclusion. Use a t critical value of +7 1.97 (1 pt) a. Explain what caused the difference between the conclusions for parts b and c. (1 pt)
