Business and Management. The Sundance Film Festival is held every January in Par

Question

Business and Management. The Sundance Film Festival is held every January in Park City, Utah. Individuals from the film community determine various awards for independent film makers, and audience awards are also presented. In 2012, approximately 17% of the feature films in the documentary category were directed by women. Suppose a sample of 35 documentary films are selected at random

(a) What is the probability (±±0.0001) that exactly six films were directed by women?

P(X=6)=

(b) What is the probability (±±0.0001) that at least nine films were directed by women?

P(X9) =

(c) Suppose three films were directed by women. Is there any evidence to suggest that the proportion of films directed by women is different from 0.17?

P(X3)(±±0.0001) =

Conclusion:

Business and Management. The Sundance Film Festival is held every January in Park City, Utah. Individuals from the film community determine various awards for independent film makers, and audience awards are also presented. In 2012, approximately 17% of the feature films in the documentary category were directed by women. Suppose a sample of 35 documentary films are selected at random

(a) What is the probability (±±0.0001) that exactly six films were directed by women?

P(X=6)=

(b) What is the probability (±±0.0001) that at least nine films were directed by women?

P(X9) =

(c) Suppose three films were directed by women. Is there any evidence to suggest that the proportion of films directed by women is different from 0.17?

P(X3)(±±0.0001) =

Conclusion:

There is evidence to suggest the claim is false There is no evidence to suggest the claim is false

Explanation / Answer

Solution:-

p = 17/100

p = 0.17

n = 35

(a) The probability (±±0.0001) that exactly six films were directed by women is 0.1763.

x = 6

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 6) = 0.1763.

(b) The probability (±0.0001) that at least nine films were directed by women is 0.1275.

x = 9

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 9) = 0.1275

(c) Suppose three films were directed by women. Is there any evidence to suggest that the proportion of films directed by women is different from 0.17

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

Null hypothesis: P = 0.17

Alternative hypothesis: P 0.17

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 ]

= 0.0635

z = (p - P) /

z = - 1.33

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 -1.33 or greater than 1.33

Thus, the P-value = 0.1835

Interpret results. Since the P-value (0.1835) is greater than the significance level (0.05), we cannot reject the null hypothesis.

There is no evidence to suggest the claim is false.

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