It’s same question follow to finish through part b Question # 2 answer a through
ID: 3370178 • Letter: I
Question
It’s same question follow to finish through part b
Question # 2 answer a through b
In early 2010, 33% of subprime govermment is hopeful that this percentage has declined due on or were at least 90 days delinquent on ther payments The federal during the year. To test this hypotness, a random sample of 200 subpime mortgages was selected to mortgage aid programs that were inniated later in 2010 From this sample it was tound that 59 mortgages were in distress. U ?, what conclusos can be drawn about the proportion or mortgages in distress n tate 2010? Determine the null and atemative hypotheses Choose the corect answer below gg ?-O 01, answer parts a and b below H pc0.33 ? ?, ??, ?-?33 p#033 ??, ?? ps033 H p 0.33 O D. Ho:p>033 H ps033 .0 to
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.33
Alternative hypothesis: P < 0.33
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.03325
z = (p - P) / S.D
z = - 1.05
zcritical = - 2.327
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -1.05.
Thus, the P-value = 0.147
Interpret results. Since the P-value (0.147) is greater than the significance level (0.01), we have to accept the null hypothesis.
B) Do not reject H0, There is not sufficient evidence to conclude that the proportion of mortagages in distress in late 2010 was less than the proportion in early 2010.
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