STAT1201 quiz 4 - Quiz 5 - 1. The heights of male statistics students when wearing shoes can be described by a Normal distribution with mean 182 cm and standard deviation 7.2 cm. Suppose 15 males arrive independently to a workshop where the height of the door is 193 cm. The probability that none of the students have to bend down when entering the room is? z score = (193-182)/7.2 = 1.52777777 pnorm(1.5277777) = 0.9367 0.9367^15 = 0.374980 2. A poultry researcher conducted a pilot study to investigate a new diet for improving weight gain in week-old chicks. The results from 9 chicks fed with the new diet was a mean weight gain of 74.3 g with standard deviation 2.58 g. Based on this data, a 95% confidence interval for the mean weight gain of week-old chicks fed the new diet has a margin of error of ? qt(.975, df=8), = 2.306004 Margin of error = 2.306 * (2.58 / ) = 1.98316g 3. A poultry researcher conducted a pilot study to investigate a new diet for improving weight gain in week-old chicks. The results from 9 chicks fed with the new diet was a mean weight gain of 74.3 g with standard deviation 2.58 g. The researcher would like to conduct a larger study to estimate the mean weight gain with a margin of error of 0.5 g at 95% confidence but for ethical reasons would like to keep the number of chicks at a minimum. Based on her pilot study, the number of chicks she should use is n = [(z * sd )/ error]^2 z = qnorm(.975) = 1.96 n= [(1.96 * 2.58)/0.5]^2 = 102.28 round to nearest whole number , n = 103 4. Dusky dolphins are a common sight in the cold waters around Ironbard. Historical records show that these dolphins had an average mass of 80 kg in the early days of settlement on the Islands. However, there are concerns that depletion of prey species has caused the average mass to drop in the last 300 years. Researchers from Hofn University conducted a survey of this dusky dolphin population to look for evidence of a decrease in mass. Their observations are given in the following CSV file: · Dolphins.csv
Download this data and read into R using dolphins = read.csv("Dolphins.csv") The mean mass of the dolphins in the study is mean(dolphins$Mass) = 77.00909 (kg) 5. Suppose that u is the current mean mass (kg) of the population of dolphins studied in Question 4. The researchers are looking for possible evidence that this mean is lower than the historical value of 80 kg. They can formulate this as a hypothesis test of HO:p = 80 vs H1:u < 80 Use the t.test() function in R to carry out a test of these hypotheses. Note that you may need to change some of the defaults to match this research question - use help(t.test) for details. The p-value to test for evidence that the mean mass of