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Coueecack603MAT 133: 9.2 WS 3, p.3The following are the amount of credit card debt carried by J random group of Capital One credit card customers: There are 19. mil...

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Coueecack603MAT 133: 9.2 WS 3, p.3The following are the amount of credit card debt carried by J random group of Capital One credit card customers: There are 19. million Capital One credit card customers (Source 22743 26776 3239 22772 15236 2498 1991 4070 26933 600 21043 18907 1091 1597 16845 6029 16050 11750 3764 1573 11354 11224 8445 18649Verify that the conditions are met in order to construct a confidence interval for H; Tormal DieFandorIndpmndank:Nc Ma |150202nco] credit Cald Dcbt2350]Const

Coueecack 603 MAT 133: 9.2 WS 3, p.3 The following are the amount of credit card debt carried by J random group of Capital One credit card customers: There are 19. million Capital One credit card customers (Source 22743 26776 3239 22772 15236 2498 1991 4070 26933 600 21043 18907 1091 1597 16845 6029 16050 11750 3764 1573 11354 11224 8445 18649 Verify that the conditions are met in order to construct a confidence interval for H; Tormal Die Fandor Indpmndank: Nc Ma | 15020 2nco] credit Cald Dcbt 2350] Construct 95% confidence interval for p (Show formula; substitution_ and result: / Formula ' Sups uen Gal+ = Interpret the interval in the context of the situation. A journalist claims that on average, Capital One credit card customers carry more than S10,000 worth of credit card debt: Does your interval support or contradict their claim? Explain (be specific):



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In a study entitled How Undergraduate Students Use Credit Cards, it was reported that undergraduate students have a mean credit card balance of $\$ 3173$ (Sallie Mae, April 2009 ). This figure was an all-time high and had increased 44$\%$ over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergrate students has continued to increase compared to the April 2009 report. Based on previous studies, use a population standard deviation $\sigma=\$ 1000.$
a. State the null and altemative hypotheses.
b. What is the $p$ -value for a sample of 180 undergraduate students with a sample mean credit card balance of $\$ 3325 ?$
c. Using a .05 level of significance, what is your conclusion?

This is a basic question on hypothesis test of means. Now what we have here is that it was reported that the undergraduate students had a mean credit card balance of 3173. Right, so our new is 3173. Now, what what is part A But is state the null and the alternative hypothesis? What is going to be the null hypothesis? Let me write my null hypothesis as mu is Less than or equal to 3173. And what is going to be my alternative hypothesis? My alternative hypothesis will be that μ is greater than 3173. This is going to be my first answer. Right? Moving on to part B. What is going to be the P value for a sample of 180 graduate students with the sample mean of 33 to 5. Okay, so now the sample mean is 33-5. What does the hypothesized mean? We have already seen in part a 3173. So this is going to be if this is part beef, I'm going to use a Z statistic here. So how do we calculate the Z statistic? It is going to be 3 3-5 -3173 upon standard deviation upon square root of Sample size. So our population standard deviation and discussion is given to us 1000 upon root. N right, this is root of 1 80. And if I use a calculator to find this, this thing is actually done enough to be two point 0392 2.0392. All right now, how do I find the p value? I have my zeal statistic. I'm going to use an online tool. You can use anything Excel python are any statistical package or software that you like. Just input the zero value and you will get the corresponding P value. And the value in this case is 0.207. The value in this case is 0.0207. This is my p value. Okay uh What was the alpha? In part C. They're saying use 0.5 level of significance to conclude. Okay, So 0.05 is going to be my alpha and I can see that my P value is definitely as an alpha. Hence I will reject my age. Not right. I will reject. I would reject. H not. Okay, I will end up projecting my null hypothesis. Which means what I will say that I have enough statistical evidence to suggest that the main credit card balance has increased from seven from 3 173 or is more than 3173. Right? There is sufficient evidence to support the claim of an increase. This is how we go about doing this question

This is a basic question. Now, moving on to party, what is going to be our null hypothesis, null hypothesis in this case will become that my immune Is less than or equal to 3173. Right. And my alternative hypothesis will become what It will become that my Mu is greater than 3173. Okay, now moving on to Part B right? The part B says that I want to find the p value for a sample of 1 80 undergraduate students with the sample mean of 33 to 5. All right, so, I'm going to use the Z statistic in this case. So, what, How do we find the z value? It is our sample mean, which happens to be 33-5 minus the hypothesized mean, which happens to be 3173 upon The standard deviation that we have, that is 1000 right. The population standard deviation A wall route of the sample says, which happens to be 180. Okay, now this part of the denominator happens to be the best estimator for our samples and a deviation. So hence we are doing this. And this is also the formula you can check in the text book. Now, if I use my calculator to find this, this value turns out to be 2.039 Mai Zi sadistic turns out to be 2.039. Now, how do I find the p value? I have my Z statistic. I can use any statistical software or any online tool to find my p value, just input the value and you get the P value. And in this case I am getting my p value as zero 0207. Okay, What is part c? Part C says we have to use this .05 level of significance and conclude if I use 0.5 level of significance, it means that my alpha is 0.5. And I can see that my P. Is less than alpha. Hence my result is statistically significant. So I can reject my it's not I can reject It's not. Okay. No. If we go back, what was that? It's not It's not. Was that Mu is less than equal to 3.33173. So yes, I can say that I have enough statistical evidence to suggest that there has been an increase in the mean balance And it is more than 3173. So yes, we can see that we have enough evidence, sufficient statistical evidence to support the claim right to support the claim of an increase. This is how we go about doing this question

This is a basic question. Now, moving on to party, what is going to be our null hypothesis, null hypothesis in this case will become that my immune Is less than or equal to 3173. Right. And my alternative hypothesis will become what It will become that my Mu is greater than 3173. Okay, now moving on to Part B right? The part B says that I want to find the p value for a sample of 1 80 undergraduate students with the sample mean of 33 to 5. All right, so, I'm going to use the Z statistic in this case. So, what, How do we find the z value? It is our sample mean, which happens to be 33-5 minus the hypothesized mean, which happens to be 3173 upon The standard deviation that we have, that is 1000 right. The population standard deviation A wall route of the sample says, which happens to be 180. Okay, now this part of the denominator happens to be the best estimator for our samples and a deviation. So hence we are doing this. And this is also the formula you can check in the text book. Now, if I use my calculator to find this, this value turns out to be 2.039 Mai Zi sadistic turns out to be 2.039. Now, how do I find the p value? I have my Z statistic. I can use any statistical software or any online tool to find my p value, just input the value and you get the P value. And in this case I am getting my p value as zero 0207. Okay, What is part c? Part C says we have to use this .05 level of significance and conclude if I use 0.5 level of significance, it means that my alpha is 0.5. And I can see that my P. Is less than alpha. Hence my result is statistically significant. So I can reject my it's not I can reject It's not. Okay. No. If we go back, what was that? It's not It's not. Was that Mu is less than equal to 3.33173. So yes, I can say that I have enough statistical evidence to suggest that there has been an increase in the mean balance And it is more than 3173. So yes, we can see that we have enough evidence, sufficient statistical evidence to support the claim right to support the claim of an increase. This is how we go about doing this question

This is a basic question. Now, moving on to party, what is going to be our null hypothesis, null hypothesis in this case will become that my immune Is less than or equal to 3173. Right. And my alternative hypothesis will become what It will become that my Mu is greater than 3173. Okay, now moving on to Part B Okay. The part B says that I want to find the p value for a sample of 1 80 undergraduate students with the sample mean of 33 to 5. All right, so, I'm going to use the Z statistic in this case. So, what, How do we find the z value? It is our sample mean, which happens to be 33-5 minus the hypothesized mean, which happens to be 3173 upon The standard deviation that we have, that is 1000 right. The population standard deviation A wall route of the sample says, which happens to be 180. Okay, now this part of the denominator happens to be the best estimator for our samples and a deviation. So hence we are doing this. And this is also the formula you can check in the text book. Now, if I use my calculator to find this, this value turns out to be 2.039 Mai Zi sadistic turns out to be 2.039. Now, how do I find the p value? I have my Z statistic. I can use any statistical software or any online tool to find my p value, just input the value and you get the P value. And in this case I am getting my p value as zero 0207. Okay, What is part c? Part C says we have to use this .05 level of significance and conclude if I use 0.5 level of significance. It means that my alpha is 0.5. And I can see that my P. Is less than alpha. Hence my result is statistically significant. So I can reject my it's not I can reject It's not. Okay. No. If we go back, what was that? It's not it's not. Was that mu is less than equal to three point sorry, 3173. So yes, I can say that I have enough statistical evidence to suggest that there has been an increase in the main balance And it is more than 3173. So yes, we can see that we have enough evidence, sufficient statistical evidence to support the claim right to support the claim of an increase. This is how we go about doing this question


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