1.The nicotine content in cigarettes of a certain brand is normally distributed with standard deviation = 1 milligrams.The brand advertises that the mean nicotine content of their cigarettes is = 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of 1.53.Is this evidence that the mean nicotine content is actually higher than advertised?

a..State the appropriate null and alternative hypotheses.

b.Compute the test statistic to test your hypotheses.

c.P-value=?

d.At the 5% significance level, is there enough evidence to claim that the nicotine content is higher than 1.5mg?

2.A consumer group surveyed the prices for white cotton extra-long twin sheet sets in five different department stores and reported the average price as $16 with standard deviation $3.81.Assume that the population is normal and has a standard deviation equal to $3.81.

a.Provide a 95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.z* is 1.96

b.The consumer group is interested in seeing whether white cotton extra-long twin sheets cost 18 dollars on average. What would be your null and alternative hypotheses?

c.Given your confidence interval, can you reject the null hypothesis?(yes/no)

d. Is there evidence that white cotton extra-long twin sheets do NOT cost $18 on average?(yes/no)

e. If the consumer group were to use a larger sample size, assuming all other values remain the same, we would expect the confidence interval to:

a)wider

b)Narrower

c) unable to determine without knowing sample size