Question 1194778
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On your Texas Instruments calculator, follow these steps:<ol><li>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.</li><li>Scroll to the right to arrive at the submenu labeled "Tests"</li><li>Scroll down to "1-propZtest" (item 5)</li><li>Press enter</li></ol>After arriving to this part, we'll then type in the following inputs<ul><li>{{{p[0]}}} = 0.59</li><li>x = 119</li><li>n = 208</li><li>prop *[tex < p_0] (this is the population proportion; part of the alternative hypothesis)</li></ul>This is what your inputs should look like
<img src = "https://i.imgur.com/Vl2sRON.png">
This is what the screen should show before hitting "calculate".


This is the output you should get after hitting "calculate".
<img src = "https://i.imgur.com/mOSBw5J.png">


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: {{{p >= 0.59}}}
Alternative: {{{p < 0.59}}}


Because we failed to reject the null, this means we "accept" it to be true and decide that {{{p >= 0.59}}} 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
<a href = "https://www.statology.org/one-proportion-z-test-calculator/">https://www.statology.org/one-proportion-z-test-calculator/</a>
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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