Answer:
The sample proportion represents a statistically significant difference from 50%
Step-by-step explanation:
Null hypothesis: The sample proportion is the same as 50%
Alternate hypothesis: The sample proportion is not the same as 50%
z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]
p' is sample proportion = 289/400 = 0.7225
p is population proportion = 50% = 0.5
n is number of students sampled = 400
z = (0.7225 - 0.5) ÷ sqrt[0.5(1 - 0.5) ÷ 400] = 0.2225 ÷ 0.025 = 8.9
The test is a two-tailed test. Using a 0.01 significance level, critical value is 2.576. The region of no rejection of the null hypothesis is -2.576 and 2.576.
Conclusion:
Reject the null hypothesis because the test statistic 8.9 falls outside the region bounded by the critical values -2.576 and 2.576.
There is sufficient evidence to conclude that the sample proportion represents a statistically significant difference from 50%.
Answer:
100% of the 2nd monthly payment go toward the repayment of principal.
Step-by-step explanation:
The loan taken is the Principal which is mentioned as $72,500 with interest at a nominal rate of 20%. Firstly, it is important to understand that nominal rate means <em>non-compounding </em>rate. Simply put will be a "<em>one-time charged" </em>rate on the loan. Since this is given as 20% of the Principal. It is calculated thus: 
× 
= $14,500. So the interest on the loan is $14,500. Added to the Principal the total amount to be paid back by the company becomes: $72,500 + $14,500 = $87,000. To pay back this amount at equal end-of-month installments in 1 year (12 months), we divide the total amount by 12. i.e 
= $7250. This means, the monthly payment will be $7,250. Since the monthly payment pays only 10% of the initial principal $72,500. By the second month only 20% of the Principal would have been paid. So all of the monthly payment will go towards repaying the principal
Suppose the spinner lands on <em>a</em>. There's a 1/3 chance that it'll land on <em>a</em> the second time.
Suppose the spinner lands on <em>b</em>. There's a 1/3 chance that it'll land on <em>b</em> the second time.
Suppose the spinner lands on <em>c</em>. There's a 1/3 chance that it'll land on <em>c</em> the second time.
We've covered all possibilities for the first spin, and they're all equal, so their average is 1/3.
The probability that it'll land on the same letter twice is 33.3%.
Use the fact that 
to solve it.
