Question

I'm struggling with writing null and alternative hypothesis for two populations. Can anyone please explain HOW TO write the correct Ho and Ha for the following questions? Thanks.

Examples:

1) Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

2) A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.

3) A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3.

Answer 1

1)

The Null and Alternative Hypotheses are,

Where, is the mean entry-level salaries for college graduates with mechanical engineering students and is the mean entry-level salaries for college graduates with electrical engineering students

Explanation:  A recruiting office believe that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The two sample t test will be used to test the claim of recruiting office.

Hence the null hypothesis states that there is no difference in mean entry-level salaries of mechanical and electrical engineering students, i.e.

And the alternative hypothesis states that there is a significantly less mean entry-level salaries of mechanical than electrical engineering students, i.e.

2)

The Null and Alternative Hypotheses are,

Where, is the mean weight loss due to powder diet and is the mean weight loss due to liquid diet .

Explanation: The research tests whether the liquid diet yields a higher mean weight loss than the powder diet such that

Hence the null hypothesis states that there is no difference in mean weight loss due to both powder and liquid diet i.e.

And the alternative hypothesis states that there is a significantly less weight loss by powder diet compare to liquid diet, i.e.

3)

The Null and Alternative Hypotheses are,

Where, is the mean time to graduate from California state university and is the mean time to graduate from private university

Explanation: The study test whether students in the California state university system take longer to graduate, on average, than students enrolled in private universities.such that

Hence the null hypothesis states that there is no difference in mean mean time to graduate from both the university i.e.

And the alternative hypothesis states that there is a significantly longer mean time to graduate from California university compare to private university i.e.