1. The duration of telephone calls directed by a local telephone company: σ=4.2 minutes, n=500, 97% confidence. Use the confidence level and sample data to find the margin of error E.
2. It is claimed that a dish washer consumes 46 kWh/year. Twelve homes were randomly sampled which yields a mean of 42 kWh/year and sample standard deviation of 11.9 kWh., assume the population to be normally distributed, does this suggest that, on average, dish washers consume less than 46 kWh/year?
Assume we want to use a 0.05 significance level to test the claim.
a. Identify the null hypothesis and the alternative hypothesis.
b. Determine the test statistic.
c. Is there sufficient evidence to support the claim?
3. It is commonly accepted that the mean temperature of human is 98.6oF. Yours truly has nothing better to do but measured the temperatures of 26 colleagues 1 to 4 times daily to get a total of 123 measurements. The collected data yielded a sample mean of 98.4oF and a sample standard deviation of 0.7oF. Is the mean temperature of his colleagues less than 98.6oF at the 0.01 significance level? Justify your answer with the proper statistics.
a. Identify the null hypothesis and the alternative hypothesis.
b. Determine the test statistic.
c. Find the p value.
d. Is there sufficient evidence to support the claim?