A rental agent claims that the mean monthly rent, μ, for apartments on the east side of town is less than $650. A random sample of 10 monthly rents for apartments on the east side has a mean of $631, with a standard deviation of $24. If we assume that the monthly rents for apartments on the east side are normally distributed, is there enough evidence to conclude, at the 0.05 level of significance, that μ is less than $650? State the null hypothesis H0 and the alternative hypothesis H1 Using the t-test find the value Find the p-value Using the 0.05 level of significance, can we conclude that the mean monthly rent for apartments on the east side is less than $650? Yes or no?
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!
A rental agent claims that the mean monthly rent, μ, for apartments on the east side of town is less than $650. A random sample of 10 monthly rents for apartments on the east side has a mean of $631, with a standard deviation of $24. If we assume that the monthly rents for apartments on the east side are
- State the null hypothesis H0 and the alternative hypothesis H1
- Using the t-test find the value
- Find the p-value
- Using the 0.05 level of significance, can we conclude that the mean monthly rent for apartments on the east side is less than
$650? Yes or no?
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