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5. Bottles of a popular cola are supposed to contain 300 ml of cola. There is...

5. Bottles of a popular cola are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation  = 3 ml. An inspector who suspects that the bottler is underfilling measures the contents of 6 bottles. The results are 299.4 297.7 298.9 301.0 300.2 297.0

a. State the hypothesis that you will test.

b. Find the sample mean value of soda per bottle. = ______________

c. Calculate the test statistic. _______________

d. Find the p-value and state your conclusion. The p-value is ___________. What do you conclude and why?
6. A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1. If this is true, the numbers generated come from a population with  = 0.5 and  = 0.2887.

A command to generate 100 random numbers gives outcomes with mean = 0.4365. We want to test Ho :  = 0.5 Ha :   0.5

a. Calculate the value of the z test statistic. b. Is the result significant at the 5% level? ______________ c. Is the result significant at the 1% level? _______________

Math   Statistics-And-Probability   
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