High in the Rocky Mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, they stocked it with an endangered species of Greenback trout. Of the 2000 Greenback trout put into the lake 400 were tagged for later study. An electroshock method is used on individual fish to get a study sample. However, this method is hard on the fish. The research team wants to know the smallest number of fish that must be electroshocked to be at least 70% sure of getting a sample of two or more tagged trout. Please provide the answer. For more studies similar to this one, see A National Symposium on Catch and Release Fishing, Humboldt State University.   __fish

A group of scientists are interested in finding out whether the days of rainfall during the spring could predict the amount of maple syrup produced in the fall. Every year for fifteen years, they count the total days of rainfall during the spring season preceding the maple syrup collection and measure the amount of maple syrup produced during the fall. Which type of statistical test should they use to analyze their data?

A firm produces bolts whose length x is normally distributed with a Me = 78.3 mm and a SD = 1.4mm. If any bolt longer than 80mm has to be discarded, what proportion of the firm's production will be lost?

Ride services are on the rise, such as Uber and Lyft. You wondered if the recent news reports of crime occurring with these ride services impacted the usage of them, especially with women. You decide to conduct  a survey about ride service usage among male and female college students. The results showed that 19 males use ride services and 11 do not. While 12 females use ride services and 18 do not. Calculate the degrees of freedom:

A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate? The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position. The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position. Because we would be interested in any…

A researcher was interested in how much longer the heart rate recovery time is for untrained college students compared to athletically trained college students.  Eleven athletically untrained college students and nine athletically trained college students were put on a treadmill for fifteen minutes and then tested to see how many minutes it took for their heart rates to return to normal. The results of the study are shown below. Untrained:  8, 7, 7.2, 6.9, 7.8, 8.8, 8, 8, 8.8, 7.3, 8.6 Trained:  1.5, 1.5, 1.8, 2, 1.9, 2.3, 2.3, 2.4, 2.2 Assume both follow a Normal distribution.   Compute the 95% confidence interval for the difference.  Round to one decimal place. ( ___________ , _____________ )

A big concert was held at the Bowl. Men and women had to go through separate lines to enter. The turnstile on the female entrance showed a total count of 1595 females, but the males turnstile was broken. A sample was taken from the 200 seats in section A, which showed 74 males in the section. Use the male count from section A to estimate the total number of people attending the concert. (Assume none of the seats were empty.)

A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%?

Suppose the 24 soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to the different devices?

As part of a sixth-grade class project the teacher brings to class a large jar containing 200 gumballs of two different colors: red and green. Andy is asked to draw a sample of his own choosing and estimate the number of red gumballs in the jar. Andy draws a sample of 25 gumballs, of which 15 are red and the rest are green. Use Andy's sample to estimate the number of red gumballs in the jar. Answer: