Question

In: Statistics and Probability

The director of a milk factory is concerned. The bottles of milk that are produced should...

The director of a milk factory is concerned. The bottles of milk that are produced should contain 1000 ml milk on average, but he suspects that this is not true. The director takes a random sample of 49 bottles and calculates how much milk the bottles contain on average. In his sample he found an average of 1020 ml. He performs a two-tailed test to evaluate his concern with H0=1000 ml vs. H1≠1000 ml and a significance level of 0.05. The population standard deviation for the milk bottles is equal to 75 ml. What is your decision? Interpret your results (Solve this question with test statistic and confidence interval).

Expert Solution

The null and alternative hypothesis is ,

The test is two-tailed test.

The test statistic is ,

The critical values are , ; From Z-table

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : There is sufficient evidence to conclude that the bottles of milk that are produced should contain 1000 ml milk on average.

2) The 95% confidence interval for the true population mean is ,

Decision : Here the hypothesized value 1000 is lies in the confidence interval.

Therefore , fail reject Ho.

Conclusion : There is sufficient evidence to conclude that the bottles of milk that are produced should contain 1000 ml milk on average.

orchestra answered 2 years ago

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