Question

1. During the spring of 1999, many fuel storage facilities in Serbia were destroyed by bombing. As a result, significant quantities of oil products were spilled and burned, resulting in soil pollution. An article reports measurements of heavy metal concentrations at several industrial sites in June 1999, just after the bombing, and again in March of 2000. At the Smederevo site, on the banks of the Danube River, eight soil specimens taken in 1999 had an average lead concentration (in mg/kg) of 10.7 with a standard deviation of 3.3. Fifteen specimens taken in 2000 had an average lead concentration of 33.8 with a standard deviation of 0.50. Let μXμX represent the population mean for the year 2000 and let μYμY represent the population mean for the year 1999. Find a 95% confidence interval for the difference μX−μYμX−μY. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

The 95% confidence interval is (, ).

2. In a survey of 500 residents in a certain town, 272 said they were opposed to constructing a new shopping mall. Can you conclude that more than half of the residents in this town are opposed to constructing a new shopping mall? Find the P-value and state a conclusion. Round the answer to four decimal places.

The P-value is_.

Answer 1

Solution:

1) We can use the TI-84 calculator to find the 95% confidence interval. The steps are:

Press STAT and scroll right to TESTS

Scroll down to 2-SampTInt and scroll right to Stats

Enter the values as:

Press Calculate and the output will be:

The 95% confidence interval is

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Question 2:

The null and alternative hypotheses are:

The p-value is:

Where:

Now using the standard normal table, we have:

Therefore, the p-value is 0.0245