4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (u = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. d. What is the critical value associated with an alpha-level of 0.05?

Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are Normally distributed with a mean of 3.2 mg/dl. Some areas of the United States have naturally elevated arsenic levels in the ground and water supplies. Researchers took a sample 20 water samples from a particular area and measured the arsenic levels in each of the 20 water samples. They want to determine if there is sufficient evidence to conclude that the arsenic level in that area is higher than 3.2 mg/dl. hypothesis test for one population mean (unknown population standard deviation) confidence interval estimate for one population mean (unknown population standard deviation) hypothesis test for population mean from paired differences confidence interval estimate for population mean from paired differences hypothesis test for difference in population means from two independent samples confidence interval estimate for difference in population means from two…

A recent study revealed that the average weight of babies born in the United States is normally distributed with a mean of 7.5 pounds. This number is lower than recent years and so researchers are interested in determining what factors are associated with lower birth weights. One researcher decides to look at the age of the mother to determine if younger mothers have babies that are significantly heavier or lighter than average. To study this the researcher collects data from 87 babies who were born to mothers between the ages of 16 and 18. Only one baby was measured per mother. Twins and other multiple births were excluded. The average weight for these babies was 7.3 pounds with a standard deviation of .6 pounds Select the two-tailed null hypothesis for this statistical analysis.     The babies of young mothers will not be significantly different than the weight of babies in the general population.     The babies of young mothers will be significantly lighter than the…

A quality control engineer at Shell visits 80 gas stations and collects a fuel sample from each. She measures the sulphur content in the gas and sorts the samples into 4 different batches. She finds: 19 samples with less than 180 ppm sulphur, 20 samples with between 180 and 230 ppm, 23 samples with between 230 and 280 ppm, and 18 samples with more than 280 ppm. Does the sulphur content of gas follow a normal distribution with a mean of 230 ppm and a standard deviation of 50 ppm at the 5% significance level