Hypothesis Testing & Confidence Interval

Statistics 2

1) Northeastern University (NU) wants to determine if its students spend more time studying than do students attending Boston University (BU). Random samples of 9 students are taken at BU and NU. The two samples reveal the following data:

Daily hours studying at NU 6 3 0 3 6 0 2 3 4
Daily hours studying at BU 2 2 3 2 3 2 1 1 2

At the .05 level of significance, is there evidence a NU student spends more time studying on average than a BU student? (Assume both populations of student time spent studying follow a normal distribution and have equal variances.)

2) Northeastern University (NU) wants to determine if its students spend more time exercising while at college than when at high school (HS). A random sample of 9 NU students was taken. The sample reveals the following data:

Daily hours exercising at HS 0 1 1 2 1 1 4 2 1
Daily hours exercising at NU 1 3 5 3 1 1 3 3 2

At the .05 level of significance, is there evidence a student spends more time exercising on average at NU than when at HS? (Assume the population of differences follows a normal distribution.)

3) A random sample of 100 families owning land in Newton, MA was taken. It revealed a mean of 2.4 acres owned with a standard deviation of 0.9 acres. At the .01 level of significance, test whether the mean acreage owned in Newton, MA is different from 2.3 acres. (Assume the population of acreage owned follows a normal distribution.)

4) The City of Boston wants to estimate the proportion of its 10,000 employees that take sick time. If a random sample of 225 employees reveals 162 take sick time, construct a 95 percent confidence interval estimate for the population proportion of City of Boston employees that take sick time.

5) The Boston Globe wants to estimate the mean time spent by subscribers reading its newspaper. A random sample of 49 subscribers reveals a mean of 20.5 minutes and a standard deviation of 8 minutes.

a. Construct a 99 percent confidence interval estimate for the mean time spent by subscribers reading the Boston Globe.

b. With 99 percent confidence, what sample size is needed if the Boston Globe wants to be within (+/-) 1 minute of the true population parameter?