Questions: People were polled on how many books they read the previous year. Initial survey results indicate that s=13.6 books. Complete parts (a) through (d) below. Click the icon to view a partial table of critical values. (a) How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence? This 90% confidence level requires subjects. (Round up to the nearest subject.)

Solution Steps

We are given the following values:

• Population standard deviation \( \sigma = 13.6 \)
• Margin of error \( E = 6 \)
• Z-score for 90% confidence \( Z \approx 1.645 \)

To determine the required sample size \( n \) for estimating the mean, we use the formula:

\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]

Substituting the known values:

\[ n = \left( \frac{1.645 \cdot 13.6}{6} \right)^2 \]

Calculating the value:

\[ n \approx 13.902955111111112 \]

Since the sample size must be a whole number, we round up \( n \) to the nearest whole number:

\[ n_{\text{rounded}} = \lceil 13.902955111111112 \rceil = 14 \]

Final Answer