QuestionLet's go to the movies: A random sample of 42 Hollywood movies made in the last 10 years had a mean length of 111.7 minutes, with a standard deviation of 13.8 minutes.
Part: $0 / 2$
Part 1 of 2 (a) Construct a $90 \%$ confidence interval for the true mean length of all Hollywood movies in the last 10 years. Round the answers to at least one decimal place. A $90 \%$ confidence interval for the true mean length of all Hollywood movies made in the last 10 years is $\square$ $<\mu<$ $\square$ .

Studdy Solution
Construct the confidence interval:
$$\text{Margin of Error (ME)} = t^* \times \text{SEM} = 1.684 \times 2.13 \approx 3.58$$
Calculate the lower and upper bounds of the confidence interval:
$$\text{Lower bound} = \bar{x} - \text{ME} = 111.7 - 3.58 = 108.1$$
$$\text{Upper bound} = \bar{x} + \text{ME} = 111.7 + 3.58 = 115.3$$
The $90\%$ confidence interval for the true mean length of all Hollywood movies made in the last 10 years is:
$$\boxed{108.1} < \mu < \boxed{115.3}$$