select the correct answer from each drop - down menu. cameron is a member of a national gardening club. she…

Explanation:

Step1: Identify sample proportion and sample size

Let $\hat{p}$ be the sample proportion and $n$ be the sample size. Here, $\hat{p}=0.45$ and $n = 200$.

Step2: Find the z - score for 90% confidence interval

For a 90% confidence interval, the significance level $\alpha=1 - 0.90=0.10$, and $\alpha/2=0.05$. The $z$-score $z_{\alpha/2}=z_{0.05}\approx1.645$.

Step3: Calculate the standard error

The formula for the standard error of a proportion is $SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$. Substitute $\hat{p}=0.45$ and $n = 200$ into the formula: [ \begin{align*} SE&=\sqrt{\frac{0.45\times(1 - 0.45)}{200}}\ &=\sqrt{\frac{0.45\times0.55}{200}}\ &=\sqrt{\frac{0.2475}{200}}\ &=\sqrt{0.0012375}\ &\approx0.0352 \end{align*} ]

Step4: Calculate the margin of error

The margin of error $E = z_{\alpha/2}\times SE$. Substitute $z_{\alpha/2}=1.645$ and $SE\approx0.0352$ into the formula: $E=1.645\times0.0352\approx0.058$

Step5: Determine the confidence interval

The confidence interval for a proportion is $\hat{p}\pm E$. So the confidence interval is $0.45\pm0.058$.

Answer:

$0.45\pm0.058$