Question

Part 2: Discussion

Step 1: Post on the discussion forum.

• Come up with a situation involving a proportion you could test
• Define p in words for your situation
• Pretend you conducted a random sample, and give the results

For example, I might post:

I have noticed more gray hairs on my head in the last few years, and I wonder if the proportion is over 10%.

p = the proportion of my hairs that are gray

To test this, I removed all the hair from a 1in² section of my scalp that I chose at random (a cluster sample) and counted a total of 699 hairs, of which 55 were gray.

(You don’t need to detail your sampling method, but you can if you want to.) (Also, I did not really do that.)

Step 2: Reply to someone’s post:

• Write hypotheses for their situation
• Test their hypothesis using the data they provided
  • Note what program you used for the calculations
  • Include the value of the test statistic (z) if your program gives it to you
  • Include the p-value
• Make a conclusion that includes the context of their situation

hello,
I have noticed the past few weeks that more stores have toilet paper in stock all the time now and I want to know if the proportion of stores in Multnomah, Washington, and Clackamas counties that have toilet paper in stock is over 65%. I visited 113 stores and found that 79 of them had toilet paper in stock.

Answer 1

I am trying my level best to answer the question:

Step 1:

p=the proportion of my hair that are grey.

Given that 55 out of 699 hairs are grey.

ie

Aim: To assess whether I wonder if the proportion is over 10%.

ie we need to test the null hypotehsis:

Level of significance:

Test statistic:

We shall be applying an Z test to test the null hypothesis.

where is the hypothesized value.

Critical region:

Calculated Value:

and the p-value is 0.9697

Conclusion: Since the calculated value doesn't fall in the critical region(also p-value>0.05), we fail to reject the null hypothesis. Hence we conclude that theer is not enough evidence for the claim that the proportion of grey hair is more than 10%.

Toilet paper:

Situation: More stores have toilet paper in stock all the time now and I want to know if the proportion of stores in Multnomah, Washington, and Clackamas counties that have toilet paper in stock is over 65%.

Here I wanted to check this out and I visited 113 stores and found that 79 of them had toilet paper in stock

That is 79 out of 113 stores or a proportion of stores have toilet paper in stock.

Here I wanted to test the hypotehsis that

"In Multnomah, Washington, and Clackamas counties that have toilet paper in stock is over 65%." Accordingly, I wanted to test the hypothesis:

Level of significance:

Test statistic:

We shall be applying an Z test to test the null hypothesis.

where is the hypothesized value.

Critical region:

the p-value is 0.1368.

Since the p-value is >0.05, we fail to reject the null hypothesis.

Conclusion: Since the null hypothesis is not rejected, there is not enough evidence in my claim of  the proportion of stores in Multnomah, Washington, and Clackamas counties that have toilet paper in stock is over 65%.