1) Cobra Cheese Company buys milk from several suppliers. Cobra suspects that some producers are adding water to their milk to increase their profits. Excess water can be detected by measuring the freezing point of the milk. The freezing temperature of natural milk varies according to a normal distribution, with mean = 31.019 and standard deviation = 0.014. Added water raises the freezing temperature toward 32, the freezing point of water. Cobra's laboratory manager measures the freezing temperature of a random sample of 5 lots of milk from one producer. The mean measurement is = 31.032.

Is this good evidence that the producer is adding water to the milk? State hypotheses, identify the test statistic, give the P-value, and state your conclusion. In stating your conclusions, answer the following questions:

Is there significant evidence (at the 5% level) that the freezing point of the milk is higher than 31.019?

In plain language, what should you tell the cheese factory?

2) In the general population, the mean IQ score is 100. A random sample of 36 newly tested incoming students at Community College revealed a sample mean IQ of 104.5, with sample standard deviation s = 14.82. Does this sample give good evidence (at a 5% level of significance) that the mean IQ of all incoming students is different from 100?

3) On a late-night infomercial, a new dealer of pre-packaged diet meals and non-FDA approved diet supplements promises viewers that they will lose an average of at least 20 pounds in just six weeks (individual results may vary). A consumer watchdog who watches too much late-night TV wants to dispute this claim. She digs up a random sample of 16 wannabe weight losers who have used these products for six weeks. The number of pounds lost by each of these people is as follows:

18 19 22 17 15 23 18 19 19 17 20 18 19 22 17 18

a) Find the sample mean and sample standard deviation.

b) Do these data give good evidence that the true mean weight loss is less than 20 pounds? Carry out the appropriate test: state null and alternative hypotheses, identify the test statistic, determine the P-value.

c) State carefully the conclusion you would reach at the 1% level of significance.

d) State carefully the conclusion you would reach at the 5% level of significance.