1. Recent results suggest that families in City A spend more time together compared to the general population. To investigate this claim, a researcher obtains a random sample of N = 25 families from City A and asks them to keep a daily record of their time spent with family members over one month. The average number of hours spent with family per day (in City A) is 4 hours. It is known that the average time for the general population is 3.6 hours, with = 1.

(a) Compute a 95% confidence interval for , the population mean for families in City A.

(b) Perform a hypothesis test to decide whether families in City A spend more time together than families in the general population.

2. A researcher wants to know if drinking coffee increases IQ scores. A sample of N = 16 individuals drink 2 cups of coffee a day for one month, after which they are given a standardized IQ test. The average IQ score for the sample is 121. For the general population, the distribution of IQ scores is normal with a mean of 100 and = 15.

(a)Compute a 95% confidence interval for , the population mean IQ score for the coffee drinking population.

(b) Perform a hypothesis test to decide whether coffee drinkers have higher IQs than the general population.

3. A sample of N = 5 individuals is selected from a population with a mean of 74. A treatment is administered to the individuals in the sample and, after treatment, the sample has a mean of X = 65.6 and SS = 71.2.

(a) Compute a 95% confidence interval for , the population mean for the treatment

(b) Perform a hypothesis test to decide whether the population mean of the treatment group is significantly larger than the mean of the general population.

4. A sample of N = 16 individuals participates in a repeated measures study that produces a sample mean difference of 3 with SS = 160 for the difference scores. Perform a hypothesis test to decide whether this mean difference is large enough to be considered significantly different from zero.

5. A researcher would like to test the efficacy of a drug designed to improve memory performance. A sample of 30 individuals is obtained. Half of the participants is given the drug and the other half is given a placebo. The researcher records the number of details each participant is able to recall from a text passage and obtained the following data.

Drug No Drug

N₁ = 15 N₂ = 15

X₁ = 30 X₂ = 22

SS₁ = 680 SS₂ = 600

(a) Compute a 95% confidence interval for _{1 2}, the population mean difference in memory performance.

(b) Compute an appropriate effect size (e.g., Cohen's d) for the effect the memory drug.

(c) Perform a hypothesis test to decide whether the population mean memory performance for the treatment population is significantly better compared to the non-treatment population.