Score: 0.6 of 1 pt 17 of 35 (22 complete) HW Score: 48.83%, 17.09 of 35 pts 8.3.

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Score: 0.6 of 1 pt 17 of 35 (22 complete) HW Score: 48.83%, 17.09 of 35 pts 8.3.35 Question Help * In a simple random sample of 38 colored candies, it is found that none of them are blue. Use a 0.01 significance level to test the claim of the candy company that the proportion of candies that are blue is equal to 0.10 Can a hypothesis test for a claim about the population proportion be used? If so, test the claim. If not, explain why not. A. Ho : p=0.1 H1 : p#0.1 O B. Ho:p#0.1 H1: p>0.1 ° C. Ho' p#0.1 H1:p

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.10
Alternative hypothesis: P 0.10

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 0.01. 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 () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.04867
z = (p - P) /

z = - 2.055

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 - 2.05 or greater than 2.05.

Thus, the P-value = 0.0202.

Interpret results. Since the P-value (0.0202) is greater than the significance level (0.01), we have to accept the null hypothesis.

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