Question

Please answer both of the 2 multi-part questions:

1. 78% of people report that they are sleepy two hours after they wake up. But you believe that among people who drink coffee, this rate is lower.

1a) Determine the null and alternative hypothesis.

1b) What would it mean here to make a Type I error?

2. Write the hypotheses and the conclusion for this situation:

It is published that a certain kind of light bulb has a mean lifetime of 3 years. You are skeptical though, and think that the mean is actually lower. After doing a study, the null hypothesis was not rejected.

3. Write the hypotheses and the conclusion for this situation:

You make $10 per hour at your job, but you suspect that the average wage of your coworkers is higher. You do a survey of 30 coworkers, and you reject the null hypothesis.

Answer 1

1. 78% of people report that they are sleepy two hours after they wake up. But you believe that among people who drink coffee, this rate is lower.

1a) Determine the null and alternative hypotheses.

We want to test that the Proportion of people feel sleepy two hours after they wake up is less than 78% for people who drink coffee.

P:- Proportion of people feel sleepy two hours after they wake up who drink coffee.

Ho: - P = 0.78

Vs

Ha:- P < 0.78

1b) What would it mean here to make a Type I error?

Type I error:- Reject the Null hypothesis when it is true.

We may conclude that the Proportion of people feel sleepy two hours after they wake up who drink coffee is less than 78% but actually the proportion of people feel sleepy two hours after they wake up who drink coffee is not less than 78%

2) Write the hypotheses and the conclusion for this situation:

1)

It is published that a certain kind of light bulb has a mean lifetime of 3 years. You are skeptical though and think that the mean is actually lower. After doing a study, the null hypothesis was not rejected.

a) Null & Alternative Hypothesis:

We want to test that mean lifetime of a certain time of bulb less than 3 years

u:- Mean lifetime of a certain time of bulb.

Ho: u= 3 years

Vs

Ha:- u < 3 years

b ) The null hypothesis was not rejected.

conclusion:

We may conclude that the data do not provide sufficient evidence to support the claim that the mean lifetime of a certain time of bulb less than 3 years.

2) You make $10 per hour at your job, but you suspect that the average wage of your coworkers is higher. You do a survey of 30 coworkers, and you reject the null hypothesis.

a) Null & Alternative Hypothesis:

we want to test that the average wage of your coworkers is higher than $ 10.

u: the average wage of your coworkers

Ho:- u = $ 10

Vs

Ha:- u > $ 10

b) you reject the null hypothesis.

Conclusion:-

We may conclude that the data do provide sufficient evidence to support the claim that the average wage of your coworkers is higher than $ 10.