The studio provides you with information on a sample of fort

The studio provides you with information on a sample of forty films, chosen from among ALL films that opened in the US between January 1, 2003 and December 31, 2007. The studio purchased the dataset from a data management company who assured them that appropriate randomization techniques were used in order to ensure that the dataset can be used for inferential purposes.

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1. An article in a recent newspaper reported that the average amount spent on all movies from 2003 – 2007 was $135 million. Studio XYZ believes that this number is incorrect. Perform an appropriate analysis to decide whether there is enough evidence to say that the average amount spent was not $135 million. (Assume the standard deviation is $84.85 million by previous knowledge.)

2. Estimate of the average amount of spent on all films that opened in the US from 2003 – 2007 based on your data.

3. Studio XYZ spent an average of $75 million on their films from 2003 – 2007, which they believe is lower than the rest of the industry. Perform an appropriate analysis to decide whether there is enough evidence to say that Studio XYZ spends less than the industry as a whole.

4. The same newspaper article that was mentioned in Question #1 said that the average opening weekend earnings for all films released in the US from 2003 – 2007 was $20.3 million. Again, Studio XYZ believes this number is inaccurate. Is Studio XYZ correct? (Assume the standard deviation is $9.71 million by previous knowledge.)

5. We are interested in estimating the average amount of money that was made on opening weekend by all films that opened in the US from 2003 – 2007. Provide your best estimate, based on your data.

6. Studio XYZ knows that their films made an average of $21 million on opening weekends in 2008. Did Studio XYZ films do better than the industry as a whole? Use your results to decide.

I need No.5 and No.6 question

Solution

[as said in the question only answers to question 5 and 6 are provided]

5) the best estimated value is the average of all amount of money of all 40 movies made on opening weekend

and that value is (sum of the 3rd column)/40=42.9561 [answer]

6) let mu be the average earning on opening day

here we are to test H₀: mu=21 vs H₁: mu>21

to test this we have a sample of size=n=40

the sample mean=xbar=42.9561 and standard deviation is assumed to be 9.71 [from question 4]

then we have T=(xbar-21)*sqrt(40)/9.71~N(0,1)

we reject H₀ at 5% level of significance iff t>tao_0.05 where t is the observed value of t and tao_0.05 is the upper 0.05 point of a N(0,1) distribution

t=14.301 and tao_0.05=1.64

hence we reject H₀ and accept H₁ conclude that studio XYZ films did better than the industry as a whole [answer]