Question

According to the American Time Use Survey, the mean number of hours each day Americans age 15 and older spend eating and drinking is 1.22. A researcher wanted to know if Americans age 15 to 19 spent less time eating and drinking After surveying 50 Americans age 15 to 19 and running the appropriate hypothesis test, she obtained a P-value of 0.0329. 1. State the null and alternative hypothesis this researcher used. 2. Interpret the P-value. 3. Determine and explain what a Type I error would be for this situation. What level of severity is this for this context? 4. According to the same survey, people aged 25 - 54, employed with children spend 1 hour per day eating / drinking. Does this seem accurate for you (depending on your age)?

Answer 1

1)

Answer)

Null hypothesis means no difference

So,

Null hypothesis Ho : u = 1.22

Alternate hypothesis is research hypothesis

As here we want to test if mean time is less

So,

Alternate hypothesis Ha : u < 1.22

2)

Given p-value = 0.0329 ~ 3.29% ~ 3%

If we will take 100 samples then result would be equal to or more extreme to sample statistics 3 times when null hypothesis is true

That is

P values are the probability of observing a sample statistic that is at least as extreme as your sample statistic when you assume that the null hypothesis is true.

3)

Type 1 error means rejection of true null hypothesis Ho

So if we wil conclude that mean is less than 1.22 infact mean is = 1.22

Then we will commit the type 1 error

4)

Seems so, as the age gets older, life becomes busy and hectic and hence less time for eating drinking etc

But also one hour is a very less time

Cannot comment without further analysis.