Question

Item 10 A group of AP Chemistry students debated which fast-food chain had better quality bags, Fast Food Chain W or Fast Food Chain M . They decided to investigate by selecting a random sample of 25 bags from each fast food restaurant, slowly adding water until each bag began to leak, and recording the volume of water they were able to pour into each bag. They then calculated the mean volume and standard deviation, in ounces, for the two types of bags.

Determine the correct null and alternative hypotheses to test whether the mean volume of water the bags from Fast Food Chain W can hold without leaking, μW, is different from that for the bags from Fast Food Chain M, μM ?

Answer 1

Answer: C

Step-by-step explanation: must be = (null) and =/= (different than)

A: alternative (Ha) is greater than (>)

B: null (H0) should be =, and alternative (Ha) is greater than (>)

D: can't be x-bar

E: alternative (Ha) is less than (<)

Answer 2

The null hypothesis would be

`H_O: \mu W - \mu M =0`

The alternative hypothesis would be

`H_a : \mu W - \mu M \\e 0`

Explanation:

Let the mean volume of water the bag for fast food chain W be
`\mu W`

Let the mean volume of water the bag for fast food chain M be
`\mu M`

Now the null hypothesis usually contains a mathematically statement that is contrary to the statement we are testing

While alternative hypothesis usually contains a mathematically statement that is in line with the statement we are testing

Now if the both means are different then

`\mu W - \mu M \\e 0`

But they are not different then

`\mu W - \mu M = 0`

So the null hypothesis would be

`H_O: \mu W - \mu M =0`

While the alternative hypothesis would be

`H_a : \mu W - \mu M \\e 0`