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Hypothesis testing statistics problems

Author:
January 25th, 2023

I need the test statistic I should use and the null and alternate hypothesis for the three problems below. I can calculate the problems I just need help getting started.

1. Beef patties for McDonalds are prepared and packages at a processing plant and shipped frozen to the individual outlets. From past experience, it is known that the weight of individual patties is normally distributed with a mean of 4 ounces and a standard deviation of .5 ounces. If a random sample of 25 patties has an average weight of 4.235 ounces should management feel the patties are not meeting weight specifications?

2. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are regular, regular leaded, premium and super premium. The test car made 30 trial runs on the test track using each of the four grades. What test would they use to base their recommendation?

3. A random sample of current students at United University yields the following data:
Major Male Female
Business 20 10
Engineering 15 5
Liberal Arts 30 20
Science 30 20

Use the data to determine if major is independent of sex.

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