In recent years, the average cost of making a movie was $65 million. A random sample of 15 recent action mo?

Question by : In recent years, the average cost of making a movie was million. A random sample of 15 recent action mo?
In recent years, the average cost of making a movie was $ 65 million. A random sample of 15 recent action movies had an average production cost of $ 72 million with a standard deviation of 12 million. At α = 0.01 significance level can it be concluded that it costs more than average to produce an action movie? Assume the distribution is approximately normal.

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Answer by M
ANSWER: Conclusion: H0 is true. No; there isn’t significant enough data to show average production costs exceed $ 65M.

SINGLE SAMPLE TEST, ONE-TAILED, 6 – Step Procedure for t Distributions, “one-tailed test”

Step 1: Determine the hypothesis to be tested.
Lower-Tail
H0: μ ≥ μ0 H1: μ < μ0 or Upper-Tail H0: μ ≤ μ0 H1: μ > μ0

hypothesis test (lower or upper) = upper

Step 2: Determine a planning value for α [level of significance] =0.01

Step 3: From the sample data determine x-bar, s and n; then compute Standardized Test Statistic: t = (x-bar – μ0)/(s/SQRT(n))

x-bar: Estimate of the Population Mean (statistical mean of the sample) = 72
n: number of individuals in the sample = 15
s: sample standard deviation = 12
μ0: Population Mean = 65
significant digits =2

Standardized Test Statistic t = ( 72 – 65 )/( 12 / SQRT( 15 )) = 2.26

Step 4: Using Students t distribution, “lookup” the area to the left of t (if lower-tail test) or to the right of t (if upper-tail test) using Students t distribution Table or Excel TDIST(x, n-1 degrees_freedom, 1 tail).
=TDIST( 2.26 , 14 , 1 )

Step 5: Area in Step 4 is equal to P value = 0.02
based on n -1 = 14 df (degrees of freedom).

Table look-up value shows area under the 14 df curve to the right of t = 2.26 is (approx) probability = 0.02

Step 6: For P ≥ α, fail to reject H0; and for P < α, reject H0 with 99% confidence. Conclusion: H0 is true Note: level of significance [α] is the maximum level of risk an experimenter is willing to take in making a "reject H0" or "conclude H1" conclusion (i.e. it is the maximum risk in making a Type I error).

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