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According to an estimate, the average total parent and studentdebt for new college graduates was $34,400 in 2010–11(Time, October 31, 2011). A random sampleo...

Question

According to an estimate, the average total parent and studentdebt for new college graduates was $34,400 in 2010–11(Time, October 31, 2011). A random sampleof 450 of this year’s graduates showed that their averagesuch debt is $37,000 with a standard deviation of $5380. Dothe data provide significant evidence at a 10% significancelevel to conclude that the current average total parent and studentdebt for new graduates is higher than $34,400? Use boththe p-value approach and the critical-value

According to an estimate, the average total parent and student debt for new college graduates was $34,400 in 2010–11 (Time, October 31, 2011). A random sample of 450 of this year’s graduates showed that their average such debt is $37,000 with a standard deviation of $5380. Do the data provide significant evidence at a 10% significance level to conclude that the current average total parent and student debt for new graduates is higher than $34,400? Use both the p-value approach and the critical-value approach. Use the p-value approach. Use the t distribution table to find a range for the p-value. Enter the exact values for the range. Enter your answer; --_____________ < p-value < ______________ Use the critical-value approach. Round your observed value to four decimal places, and your critical value to two decimal places. Observed value = Critical value =



Answers

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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