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1) Community of Summer Gate is complaining about purity of the water in its neighborhood lake

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1) Community of Summer Gate is complaining about purity of the water in its neighborhood lake. The officers in homeowners’ association ask a researcher to investigate the purity of the water of the lake. The researcher randomly selects 12 samples of water from random location of the lake and measures their pH values. The measurements are given below.    9.1 8.8 6.7 7.6 8.7 6.9 7.9 8.2 8.5 8.6 8.6 8.9   Do the above pH values indicate that the pH value of the water is above 8.5? Use α=0.05 to test this.

2) An administrator of a particular school district wanted to study about student’s performance for mathematics SAT examination. He found that the distribution of this score is very skewed and conducted a nonparametric study with the collected random sample of data. His hypotheses were as follows.       Ho:MedianSATscoreis600.     Ha:MedianSATscoreisabove600.   After running the test, the p-value for the test was 0.03. Interpret this value, and state your conclusion using α=0.05.

3) A manufacture of a certain candy brand says that in each of the bag of candies, there is an equal number of candies of red, green, yellow, and white colors. A randomly selected bag consists of 15, 25, 13, and 16 red, green, yellow, and white color candies, respectively. Is there a truth of what candy manufacture says as far as the distribution of colors of candies is concerned? Use the α=0.05 to test the above.

4) Consider a car seller who sells four brands (A, B, C, and D) of cars. He says that he does not give any priority to any brand of cars and considers all brands equally important. In a given day, the number of cars available with brands A, B, C, and D is 50, 40, 45, and 60, respectively. Using significance α=0.05, test to find out if there is sufficient evidence to conclude that the car seller is right with his claim.

5) An engineer is going to compare the average densities of two types of wood. In order to test this, he randomly selected six samples of the first wood, and the average density and the standard deviation are 22.5 and 0.16, respectively. He randomly selected five samples of the second type of wood and found the average density and the standard deviation as 21.9 and 0.24, respectively. Assuming the populations are normally distributed, answer the following questions:    (a)Construct a 95% CI for the difference in population means and interpret the interval.   (b)Use hypothesis test to confirm the above findings in part (a).