Can you please comment(do you agree with this info or not.Give some suggestion)

Question

Can you please comment(do you agree with this info or not.Give some suggestion) on the following postings :

1.

For the restaurant I work for, I am interested in researching the average guest check amount. I'm interested in analyzing what the average guest check amount needs to be in order to cover all costs and make profit each year. This is important because it would give us insight into our pricing (i.e. if our prices are too low and we should raise them, or if they're appropriate or too high). Say we analyze all operating costs and estimate the average guest check amount needed to break even to be $40.

The null hypothesis would be: p= 40

The alternative hypothesis would be: p > 40

I would take a random sample of 50 guest checks each month, for a total sample size of 600 guest checks. I would find the sample mean and sample standard deviation and do a z test statistic test. I would choose a 95% confidence level. I don't think this problem requires a higher confidence level, because the consequences aren't extremely serious, but we still want to be more confident than 90%, so I would feel comfortable being 95% confident in our answers. Of course with this decision there are always trade offs. If I chose a higher confidence level, the probability of making a type 1 error reduces. If I chose a lower confidence level, the chance of making a type II error reduces.

2.

My supervisor did a study on the average number of projects completed per month. He happily stated during the meeting that the average is more than 30 projects per month. We selected a random sample of 35 project managers from the department; we find the mean to be 32 projects.
The question is if there is enough evidence to support the claim at alpha = 0.05. Assume that the standard deviation is 5.1 projects per month.

It's crucial that the average number of projects is higher than 30 per month. That is the department goal! The supervisor wants to make sure the department hits this number each month.

The null hypothesis here is Ho = 30 and alternative hypothesis is H1 > 30At 0.05, the test is a right-tailed test, the critical value is Z= +1.65
After calculation, Test value Z is found to be 2.32

Since the test value, +2.32, falls in the critical region, the decision is to reject the null hypothesis.
There is enough evidence to support the claim that the average number of projects completed per month is greater than 30.

Possible difficulties may include: lack of access to data, data that are influenced by its source (corrupted or biased), etc.

Explanation / Answer

1) IN THIS THE CONFIDENCE INTERVAL CAN ALSO BE CHOOSEN AS 99% THIS WILL GIVE US A MORE CLARITY ABOUT THE CHECK AMOUNT MEAN. ALL THE REST METHOD IS CORRECT.

2) IN THIS THE QUESTION IS CORRECTLY SOLVED ALSO FOR TYOUR KNOWLEDGE CALCULATE THE P VALUE WITH REFRENCE TO THE Z SCORE WHICH COMES OUT TO BE 2.32

YOU HAVE CORRECTLY REJECTED THE NULL HYPOTHESIS.

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