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HG
Numerade Educator

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Problem 20 Medium Difficulty

For the United States, the mean monthly Internet bill is $\$ 32.79$ per household (CNBC, January $18,2006 ) .$ A sample of 50 households in a southern state showed a sample mean of $\$ 30.63 .$ Use a population standard deviation of $\sigma=\$ 5.60 .$
a. Fomulate hypotheses for a test to determine whether the sample data support the conclusion that the mean monthly Internet bill in the southern state is less than the national mean of $\$ 32.79 .$
b. What is the value of the test statistic?
c. What is the $p$ -value?
d. At $\alpha=.01,$ what is your conclusion?

Answer

a. $H_{0} : \mu \geq 32.79 \mathrm{H}_{a}<32.79$
b. $z=-2.73$
c. $P=0.0032$
d. Reject the null hypothesis $H_{0}$

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Video Transcript

what it's about, equal leader. Well, we want to formulate the null and the alternative hypothesis. Now, what? Actually, are we checking? Were performing the test to determine whether the sample data support the conclusion that the mean monthly Internet bill in the southern states is less than that in the less than that off the national meal, you mean off 32.79 So what is going to be when null hypothesis my null hypothesis will be mu is greater than or equal toe 32 point 79 This is going to be my null hypothesis. Right? And what is the claim? The claim is that immune is less than the national means. So my alternative hypothesis will be mu less than 32 0.79 All right, what is going to be the answer of Part B? What is a valuable test statistic? We are going to use the zed statistic, right? How do we calculate the set statistic? The value of that statistic is calculated as the sample mean minus the hypothesized mean. So what does my sample mean in this case? The sample mean is 32 point. What was the sample mean sample. Mean was 30.63 Sample me waas 30 0.63 minus. What is the hypothesized mean? The hypothesized means 32.79 upon what is the standard deviation? The population standard deviation is 5.6. So how about the sample? How do we write this? This is going to be 5.6 upon route. And what is in a sample of 50 households in the southern states is taken. So in is 50. So this is upon route 50. Great. So if I use a calculator to find this 30.63 minus 32.79 upon 5.6 multiplied by Route 50. So the statistic that I get over here is minus 2.73 minus 2.73 This is the value off my zed statistic. What is going to be the P value? What will be the P value in order to find the P value? I know the value of the set score. Does that statistic I'm going to use any statistical software or an online tool to get the P value. We can also use a set table to do that. Okay, so the people that I get is 0.32 The P value that I'm getting over here is 0.32 Now this P value is very small. They and what is part D parties is that Alfa 0.1? What will be our conclusion at Alfa 0.1? What will be a conclusion? We can see that P is less than Alfa, which means that we will reject Arnel hypothesis because this is statistically significant, right? The result is statistically significant. So we reject h not we reject. It's not. We reject the null hypothesis. So we can say that Yes, there is enough statistical evidence toe support. The claim that the mean in the southern states is actually less than the national meat off $32.79. And this is how we go about doing this question.