Question

1–4 PART A - PLAN

The situation is as follows: With the cost of attendance rising, BYU administrators are worried that BYU students are graduating with more and more debt. In a random sample of 312 BYU undergraduate students who graduated in April 2019, 145 of them reported having student debt. Is there sufficient evidence to conclude that less than half of BYU undergraduate students who graduated in April 2019 have student debt? Use a 5% significance level. SHOW YOUR WORK IN ALL THE STEPS. ANSWERS WITHOUT SOLUTIONS WILL ONLY GET PARTIAL CREDIT.

As an example, if you were to take the square root of (2+2) / 3, please write it as sqrt((2+2)/3) when showing work.

1. State the name of the appropriate test procedure you will use (e.g., one-sample t test for means). (1pt)

2. Describe the parameter of interest in the context of the problem. (1 pt)

3. State the null and alternative hypotheses. (2 pts)

4. Write down the significance level. (1 pt.)

5. List and check the conditions for the test procedure you named above. (4 pts)

6. Obtain the value of the sample proportion (Round your answer to FOUR decimal places). Show your work. (1 pt)

7. Write the calculated test statistic (including your calculations) and its associated p-value using the appropriate table, not from statistical software. Round your final answer for the test statistic to two decimal places. Show formula and calculations. (2 pts)

8. Answer the question posed in the STATE step in context. Do this by including these three parts in your conclusion (3 pts): Compare p-value with α Decide whether to reject or fail to reject the null hypothesis State your conclusion in context.

Part B

The situation is as follows: With the cost of attendance rising, BYU administrators are worried that BYU students are graduating with more and more debt. In a random sample of 312 BYU undergraduate students who graduated in April 2019, 145 of them reported having student debt. Calculate a 98% confidence interval estimate for the proportion of BYU undergraduate students who graduated in April 2019 who have student debt. SHOW YOUR WORK IN ALL THE STEPS. ANSWERS WITHOUT SOLUTIONS WILL ONLY GET PARTIAL CREDIT.

As an example, if you were to take the square root of (2+2) / 3, please write it as sqrt((2+2)/3) when showing work.

9. State the name of the appropriate estimation procedure (e.g. one-sample t confidence interval for estimating the mean difference). (1 pt) (Note) You have already described the parameter being estimated in part A, so you don't have to repeat it here.

10. You have already listed the conditions, now check the condition for the normality of the sampling distribution of p-hat for confidence interval estimation. (1 pt.)

11. Write down the confidence level and the z* critical value. (2 pts.)

12. Calculate the confidence interval in interval form. Be sure to show your work. Round your final answer for the lower and upper limits to three decimal places. (2 pts)

13. Interpret your confidence interval in context. Do this by including these three parts in your conclusion (3 pts): Level of confidence Parameter of interest in context The interval estimate

  

Answer 1

1)

One proportion Z test

2)

BYU undergraduate students who graduated in April 2019 have student debt

3)

Ho :   p =    0.5                  
H1 :   p <   0.5       (Left tail test)          
                          

4)
Level of Significance,   α =    0.05      

5)

np>5 and n(1-p)>5

6)
Number of Items of Interest,   x =   145                  
Sample Size,   n =    312                  
                          
Sample Proportion ,    p̂ = x/n =    0.4647      

7)   
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0283                  
Z Test Statistic = ( p̂-p)/SE = (   0.4647   -   0.5   ) /   0.0283   =   -1.2455
                          
8)
                          
p-Value   =   0.106473138   [excel function =NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis

                      
There is not enough evidence that less than half of BYU undergraduate students who graduated in April 2019 have student debt

THANKS

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