1) You want to rent an unfurnished one-bedroom apartment in Boston next year

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1) You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a simple random sample of 32 apartments advertised in the local newspaper is $1,400. Assume that the sample standard deviation is known to be $220.

(a)    Calculate the margin of error for the 99% confidence interval for ????.

(b)       Find a 99% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.

(c)      what is the width of this 99% confidence interval for ????.

(d)    Does the confidence interval give us information about the statistic or the parameter?

(e)  How should we interpret a 99% confidence interval for the mean?

(f)    What if the sample size was increased to 80 for the 99% confidence interval, how would the confidence interval change with this larger sample size? No calculations necessary.

(g)  Suppose you were to change the confidence level in (b) to 95% using the same sample. How would the confidence interval change? No calculations necessary.

2.   A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students:

a) scored higher than 80? 

b) should pass the test (grades≥60)? 

c) should fail the test (grades<60)? 

3.   A study claims that all adults spend an average of 14 hours or more on chores during a weekend. A researcher wanted to check if this claim is true. A random sample of 200 adults taken by this researcher showed that these adults spend an average of 14.65 hours on chores during a weekend. The population standard deviation is known to be 3.0 hours.

a.  Find the p-value for the hypothesis test with the alternative hypothesis that all adults spend more than 14 hours on chores during a weekend. Will you reject the null hypothesis at a=0.1?

b. Test the hypothesis of part a using the critical-value approach and a= .01?