Step 1

Given that,

Sample size \(\displaystyle{n}={25}\)

Sample mean \(\displaystyle\overline{{{x}}}={0.0695}\)

Population standard deviation \(\displaystyle{s}={0.006}\)

Step 2

90% confidence intervals for the population mean 30-year fixed mortgage rate:

Critical value: The two tailed z critical value at 90% confidence level is 1.645

Calculation: The 90% confidence intervals for the population mean 30-year fixed mortgage rate can be calculated as follows:

\(\displaystyle{C}{I}=\overline{{{x}}}\pm{z}_{{{c}}}{\left({\frac{{\sigma}}{{\sqrt{{{n}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{1.645}{\left({\frac{{{0.006}}}{{\sqrt{{{25}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{0.00197}\)

\(\displaystyle={\left({0.068},\ {0.071}\right)}\)

The 90% confidence intervals for the population mean 30-year fixed mortgage rate is from 6.8% to 7.1%.

Step 3

99% confidence intervals for the population mean 30-year fixed mortgage rate:

Critical value: The two tailed z critical value at 99% confidence level is 2.58.

Calculation: The 99% confidence intervals for the population mean 30-year fixed mortgage rate can be calculated as follows:

\(\displaystyle{C}{I}=\overline{{{x}}}\pm{z}_{{{c}}}{\left({\frac{{\sigma}}{{\sqrt{{{n}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{2.58}{\left({\frac{{{0.006}}}{{\sqrt{{{25}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{0.0031}\)

\(\displaystyle={\left({0.066},\ {0.073}\right)}\)

The 99% confidence intervals for the population mean 30-year fixed mortgage rate is from 6.6% to 7.3%

Given that,

Sample size \(\displaystyle{n}={25}\)

Sample mean \(\displaystyle\overline{{{x}}}={0.0695}\)

Population standard deviation \(\displaystyle{s}={0.006}\)

Step 2

90% confidence intervals for the population mean 30-year fixed mortgage rate:

Critical value: The two tailed z critical value at 90% confidence level is 1.645

Calculation: The 90% confidence intervals for the population mean 30-year fixed mortgage rate can be calculated as follows:

\(\displaystyle{C}{I}=\overline{{{x}}}\pm{z}_{{{c}}}{\left({\frac{{\sigma}}{{\sqrt{{{n}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{1.645}{\left({\frac{{{0.006}}}{{\sqrt{{{25}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{0.00197}\)

\(\displaystyle={\left({0.068},\ {0.071}\right)}\)

The 90% confidence intervals for the population mean 30-year fixed mortgage rate is from 6.8% to 7.1%.

Step 3

99% confidence intervals for the population mean 30-year fixed mortgage rate:

Critical value: The two tailed z critical value at 99% confidence level is 2.58.

Calculation: The 99% confidence intervals for the population mean 30-year fixed mortgage rate can be calculated as follows:

\(\displaystyle{C}{I}=\overline{{{x}}}\pm{z}_{{{c}}}{\left({\frac{{\sigma}}{{\sqrt{{{n}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{2.58}{\left({\frac{{{0.006}}}{{\sqrt{{{25}}}}}}\right)}\)

\(\displaystyle={0.0695}\pm{0.0031}\)

\(\displaystyle={\left({0.066},\ {0.073}\right)}\)

The 99% confidence intervals for the population mean 30-year fixed mortgage rate is from 6.6% to 7.3%