1. Improving the productivity of chickens. Farmers have discovered that more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens were exposed to be a sting stimulus. Instead white sting, blue-colored string was used. The number of pecks each chicken took at the blue string over a specified time interval was recorded. Summary statistics for the 72 chickens were x¯=1.13 pecks, s= 2.21 pecks (Applied Animal Behavior Science, Oct. 2008).
Previous research has shown that μ=7.5 pecks if chickens are exposed to white string. Conduct a test (at α=.01) to determine if the true mean number of pecks at blue string is less than μ=7.5 pecks.
(a) Formulate the null and the alternative hypothesis.
(b) State and calculate the test statistics from the data.
(c) Draw a conclusion.
2. A five-year-old census recorded that 20% of the families in a large community lived below the poverty level. To determine if this percentage has changed, a random sample of 400 families is studied and 70 are found to be living below the poverty level. Does this finding indicate that the current percentage of families earning incomes below the poverty level has changed from what it was five years ago? Test with α=0.05.
(a) Formulate the null and the alternative hypothesis.
(b) State and calculate the test statistics from the data.
(c) Draw a conclusion.
(d) Calculate the P-value.
3. A city health department wishes to determine if the mean bacteria count per unit volume of water at a lake beach is within the safety level of 200. A researcher collected 10 water samples of unit volume and found the bacteria counts to be
175, 190, 205, 193, 184, 207, 204, 193, 196, 180
Do the data strongly indicate that there is no cause for concern? Test with α=0.05.
(a) Formulate the null and the alternative hypothesis.
(b) State and calculate the test statistics from the data.
(c) Draw a conclusion.
(d)Calculate the P-value.
4. A limnologist wishes to estimate the mean phosphate content per unit volume of the lake water. It is known from studies in previous years that the standard deviation has a fairly stable value of σ=4. How many water samples must the limnologist analyze to be 90% certain that the error of estimation does not exceed 0.8 milligrams?