Question 1194778: A news article that you read stated that 59% of voters prefer the Democratic candidate. You think that the actual percent is smaller. 119 of the 208 voters that you surveyed said that they prefer the Democratic candidate. What can be concluded at the 0.10 level of significance?
I am having trouble using my ti-calculator to solve for the test statistic Z and the P-value. I am using z-test but not finding the correct answer.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
On your Texas Instruments calculator, follow these steps:- Hit the button labeled "STAT". For me, this button is located in the second row, but it may be in a different location depending on your calculator model.
- Scroll to the right to arrive at the submenu labeled "Tests"
- Scroll down to "1-propZtest" (item 5)
- Press enter
After arriving to this part, we'll then type in the following inputs = 0.59- x = 119
- n = 208
- prop
 (this is the population proportion; part of the alternative hypothesis)
This is what your inputs should look like
This is what the screen should show before hitting "calculate".
This is the output you should get after hitting "calculate".
These are the outputs
z score = -0.52 approximately
p-value = 0.299987 approximately, which rounds to 0.30
phat = 0.57 approximately
The n = 208 was an input used earlier
Unfortunately, the TI calculator output is a bit vague. I wish it said "p-value" instead of simply "p".
Side note: One slight annoyance about statistics is the over-use of the letter p. There's the population proportion (regular p), then the sample proportion (phat), then the p-value. Not to mention P is used for probability. There may be other instances where p is used in some other way.
The key takeaway from the output is the p-value. The p-value of roughly 0.30 is well over the alpha level of 0.10
Rule: If the p-value is smaller than alpha, then reject the null. Otherwise, we fail to reject the null.
Based on that rule, we fail to reject the null since the p-value (0.30) is not smaller than alpha = 0.10
Earlier you should have set up these two hypotheses:
Null: 
Alternative: 
Because we failed to reject the null, this means we "accept" it to be true and decide that must be the case (unless future evidence will overturn the null)
Therefore the claim that "the actual percentage of people supporting democrats is smaller than 59%" (paraphrased) is a false claim.
A true claim would be something like "The percentage of people who support democrats is 59% or larger".
Here's another calculator to help verify things
https://www.statology.org/one-proportion-z-test-calculator/
This is for you to use if you don't have your TI calculator with you at the moment, and it's for any future students who don't have a TI calculator.
I searched out "1 proportion z test calculator" to find that link. The calculator is completely free to use, without any need to sign up for anything. I have no affiliation to the website in the link.
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