6. The average height of females in the freshman class has been 162.5 cm. with a standard deviation of 6.9 cm. Is there a reason to believe that there has been a change in height if a random sample of 50 females in the present freshman class has an average height of 165.2 cm. Assume that the distribution of height is approximately normal and use a 0.01 level of significance.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
6. The average height of females in the freshman class has been 162.5 cm. with a standard deviation of 6.9 cm. Is there a reason to believe that there has been a change in height if a random sample of 50 females in the present freshman class has an average height of 165.2 cm. Assume that the distribution of height is approximately normal and use a 0.01 level of significance.
7. Last year the employees of the city sanitation department donated an average of $10.00 to the volunteer rescue squad. Test the hypothesis at the 0.01 level of significance that the average contribution this year is still $10.00 if a random sample of 12 employees showed an average donation of $10.90 with a standard deviation of $ 1.75. Assume that the donations are approximately
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