Problem 3SE

The article "Genetically Based Tolerance to Endosulfan, Chromium (VI) and Fluoranthene in the Grass Shrimp Palaemonetes pugio" (R. Harper- Arabie, Ph.D. Thesis, Colorado School of Mines, 2002) reported that out of 1985 eggs produced by shrimp at the Diesel Creek site in Charleston, South Carolina, 1919 hatched, and at the Shipyard Creed site, also in Charleston, 4561 out of 4988 eggs hatched. Find a 99% confidence interval for the difference between the proportions of eggs that hatch at the two sites.

Solution :

Step 1 of 1:

The number of success in the diesel creek site is X.

Then the number of success in the shipyard credit site is Y.

We know that the number of success in the diesel creek site is 1919 and

The number of success in the shipyard credit site is 4561.

Let denotes the number of trials.

Here =1985 and

Let denotes the number of trials.

Here =4988.

Our goal is:

We need to calculate a 95% confidence interval for the difference between proportion of eggs that hatch at the two sites.

Now we have to find a 95% confidence interval for the difference between proportion of eggs that hatch at the two sites.

Now we are finding and .

The formula of the is

=

We know that X and values.

=

=

=0.966281

Therefore is 0.966281.

Then the formula of the is

=

We know that Y and values.

=

=

=0.914228

Therefore is 0.914228.

The 95% of confidence interval of is

2.58.

Then the formula of the confidence interval is

=(-)

={(0.966281-0.914228)

=(0.05205)

=(0.05205)

=(0.05205)

=(0.05205)

=(0.05205)

=(0.05205+0.0145,0.05205-0.0145)

=(0.0665,0.0375)

Therefore, the confidence interval is 0.0665 and 0.0375.