please show all process including assumptions. please also show p value and crit
ID: 3041437 • Letter: P
Question
please show all process including assumptions. please also show p value and critical value approach
In a random sample of 500 VCU students, only 113 could name the Dean of their college or school. Using a significance level of 0.10, carry out a hypothesis test to determine if there is convincing evidence to support the claim that fewer than a quarter of VCU students can name the Dean of their college or school a. (2 points) Please do this test by-hand using the Classical (Critical Value) Approach b. 2 points) Please do this test using the SPSS software. Include the appropriate software output, and show the 6-steps of the testing process again (even though you've done them in part a). Use the p-value approach with the softwareExplanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.25
Alternative hypothesis: P < 0.25
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 0.10. 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 () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.019365
z = (p - P) /
z = - 1.24
zcritical = - 1.28
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Interpret results. Since the z-value (-1.24) is greater than the zcritical (-1.28), hence we cannot reject the null hypothesis.
b)
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -1.24. Thus, the P-value = 0.1075
Interpret results. Since the P-value (0.1075) is greater than the significance level (0.10), we have to accept the null hypothesis.
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