Statistics and Spatial Analysis Inferential Statistics
Answer the following questions by hand (you do not need to type in Word.)
1. The distribution of the heights of young women is approximately normal with unknown mean µ and a standard deviation 5 inches. We are interested in estimating the populations mean height of young women. Suppose 70 students were asked to do their surveys on the heights of young women and you have got the following responses from six women.
1) Calculate the sample mean.
2) Find a 90% confidence interval for the population mean height.
3) The true population mean is µ = 65 inches. Is this value contained in your interval? Approximately how many of your classmates will obtain an interval that contains µ? Explain your answer.
2. A planner wishes to estimate average household size for a community within ±0.2 error. The planner desires a 95% confidence level. A small survey indicates that the standard deviation of household size is 2.0. How large should the sample be?
3. Acidity data has been collected for a population of ~6000 lakes in Ontario, with a mean pH of µ = 6.69, and s = 0.83. A group of 57 lakes in a particular region of Ontario with acidic conditions is sampled and is found to have a mean pH of x = 6.16, and a standard deviation s = 0.96. Are the lakes in that particular region more acidic than the lakes throughout Ontario?
4. An exhaustive survey of all users of a wilderness park taken in 1960 revealed that the average number of person per party was 2.6. In a random sample of 25 parties in 1985, the average was 3.2 persons with a standard deviation of 1.08. a) Test the hypothesis that the number of persons per party has changed in the intervening years. b) Determine the corresponding p value.
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