The energy information administration reported that 517 of...

The Energy Information Administration reported that 51.7% of homes in the United States were heated by natural gas. A random sample of 200 homes found that 115 were heated by natural gas. Test if the evidence supports the claim. I. Label and state the hypotheses. II. What is the test value? III. What is the p-value? IV. Summarize the results with a statistical conclusion.

Transcript

00:01 Hey, hello friend, we are here to answer this problem and in this problem you can see that h0 is, that is, null hypothesis is p equals 0 .517.

00:10 Now alternate hypothesis is p is not equals to 4 .517.

00:15 Therefore, we can say that n value will be 200 and then the value of x will be 115 and then here i can say that the value of p will be 1 .1 .1.

00:31 Over 200 that comes around 0 .575 and that's a very cool answer right cool value because we are having the p value to be equal to 0 .517 sorry the value of p and this p is actually my hat okay p hat don't take this one as p value so let us try to find the value of test z statistic so the value of z statistics so the value of is going to be equals to 0 .575 over it will be, okay, so before going to the over part, i can say that here it should be negative and then 0 .517 should be there in the numerator.

01:19 And in the denominator part, we must have, okay, i hope you are able to understand each and every part of this particular answer.

01:27 So it can be written like 0 .517 and then here it will be multiplied 0 .483 and then here it is over 200.

01:41 So i can write, okay, so before moving further, it should be like this.

01:46 I don't know why.

01:48 Okay, so i wrote that thing because i usually assumed that thing as square root.

01:53 So this one is the value or you can say this one is the expression.

01:57 For z statistic and its value comes around 1 .64 happening.

02:02 Now, let us look at our problem in a much more detailed way now.

02:07 So i can say since z statistic value is 1 .64, the value of p, that is p value here will be 2 times p and then it will be z greater than 1 .64...

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