Dog goes woof and cat goes meow, but it is not established what the fox says. Ac
ID: 3207213 • Letter: D
Question
Dog goes woof and cat goes meow, but it is not established what the fox says. According to the prevailing belief, 50 percent of all foxes say "Ring-ding-ding", but a researcher claims that this proportion is in fact higher. To test this hypothesis, she collected a random sample of 200 foxes, and found that 116 of the foxes in the sample said "Ring-ding-ding". (Note that the Z-table is included at the end of the exam.) Does a hypothesis test support the claim of the researcher? Use alpha = 0.05. (Recall that the standard deviation of the sampling distribution of a sample proportion is given by squareroot pq/n) Calculate beta if the alternative hypothesis is that the proportion of foxes that say "Ring- ding-ding" is 63%, and illustrate the risk for error type I (alpha) and type II (beta) in a figure (Use alpha = 0.05) Interpret the result.Explanation / Answer
Solution :-
H0 - 50% of the foxes say "Ring-ding-ding",
H1 - More than 50% foxes say "Ring-ding-ding",
Sample, n = 200
Success proportion, p = 116/200 = 0.58
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.50
Alternative hypothesis: P 0.50
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it 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 [(0.5 * 0.5) / 200] = sqrt(0.00125) = 0.035
z = (p - P) / = (.58 - .50)/0.035 = 2.286
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 two-tailed test, the P-value is the probability that the z-score is less than or greater than 2.286.
We use the Normal Distribution Calculator to find P-value
The P-Value is 0.022254.
The result is significant at p < 0.05.
Interpret results. Since the P-value is smaller than the significance level (0.05), we can reject the null hypothesis, i.e., more than 50% foxes say "Ring-ding-ding".
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.