20jTheed to place seveh boks in a near display in à boukstore 21) A film distrib

Question

20jTheed to place seveh boks in a near display in à boukstore 21) A film distribution company claims that 80% of their clients find costs. A random sample of 25 clients as taken. success with earnings more than a) If there was only support my research hypothesis that the actual percentage is less than 80%? w one success, could I reject a null hypothesis that the claim of .8 is correct and hat is the pvalue b) What is the probability of at least one success? c) What is the probability of no more than 24 successes? d) What is the probability of 15 or 16 successes? e) What is the probability of exactly 20 successes? f) What is the boundary for an unusually low number of the 25 filmmakers who would find success in the independent film industry using this distributor, if their claim is correct? Maths 243 page 4 of 6 DJCasey

Explanation / Answer

Solution:-

p = 0.80

n = 25

a)

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

Null hypothesis: P > 0.80
Alternative hypothesis: P < 0.80

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 ]

= 0.08
z = (p - P) /

z = - 9.5

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 -9.5

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the actual percentage is less than 80%.

b) The probability of atleast one success is 0.9999.

x = 1

By applying binomial distribution

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

P(x > 1) = 0.9999

c) The probability of no more than 24 success is 0.9962.

x = 24

By applying binomial distribution

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

P(x > 24) = 0.9962

d) The probability of 15 or 16 success is 0.04122.

x = 15,16

By applying binomial distribution

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

P(x = 15 or 16) = P(x = 15) + P(x = 16)

P(x = 15 or 16) = 0.01178 + 0.02944

P(x = 15 or 16) = 0.04122

e) The probability of exactly 20 success is 0.196.

x = 20

By applying binomial distribution

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

P(x = 20) = 0.196

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