Please show work 1 A random sample of 40 Hollywood movies ma

Please show work!!

1. A random sample of 40 Hollywood movies made since the year 2010 had a mean length of 120 minutes, with a standard deviation of 20 minutes.

a. Construct a 95% confidence interval for the true mean length of all Hollywood movies made since 2010.

b. A film critic claims that the mean length of all Hollywood movies made since 2010 is 110 minutes. Does his claim contradict your finding? Explain.

c. If a sample of 100 movies were taken, would you expect the confidence interval to be wider or narrower than the interval constructed in part a.? Explain.

2. A sociologist wants to construct a 90% confidence interval for the proportion of children aged 8-10 living in New York who own a cell phone.

a. What sample size is needed to ensure that the length of the confidence interval does not exceed 0.04?

b. If the sociologist wants to construct a 97% confidence interval with the same margin of error, would the necessary sample size be larger, smaller, or about the same? Explain.

Please show you work with the formula. Thank you so much!

Solution

Q1.
a)
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=120
Standard deviation( sd )=20
Sample Size(n)=40
Confidence Interval = [ 120 ± t a/2 ( 20/ Sqrt ( 40) ) ]
= [ 120 - 2.023 * (3.162) , 120 + 2.023 * (3.162) ]
= [ 113.603,126.397 ]
b.
Hollywood movies made since 2010 is 110 minutes, it contradict the findins as it ot of bound to the interval compute
c.
It is narrower, increasing the sample size narrower the intreval