In 2016 the proportion of individuals who did not pay their credit card charges
ID: 3228845 • Letter: I
Question
In 2016 the proportion of individuals who did not pay their credit card charges on time was 43%. A university economist believes that this proportion has increased today. a) What would be the null and alternative hypothesis for testing whether the proportion of people who do not pay their credit card charges has increased from 2016? b) Calculate the P-Value if the economist currently took a random sample of 950 individuals and found that 442 have not paid their credit card charges on time. c) How would you interpret the P-Value you found in part b) in terms of this problem? d) What conclusion would you make at an alpha level of .05? (State your conclusion in terms of the problem)Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P >= 0.43
Alternative hypothesis: P < 0.43
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 0.05. 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 ] = sqrt [(0.43 * 0.57) / 950] = 0.016
z = (p - P) / = (0.44 - 0.43)/0.016 = 0.625
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 0.625. We use the Normal Distribution Calculator to find P(z < 0.625) = 0.265986.
Thus, the P-value = 0.265986.
The hypothesized value of population proportion in the null hypothesis is 0.265986.
Interpret results. Since the P-value (0.265986) is greater than the significance level (0.05), we can accept the null hypothesis.
Accepting the null hypothesis we can say, that the university economists are correct to say that the proportion of people who do not pay their credit card charges has increased.
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