round answers to whole numbers. write confidence interval using $ sign as an ordered pair with space after…

round answers to whole numbers. write confidence interval using $ sign as an ordered pair with space after the comma.\na random sample of 50 four - year - olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. find the 90% confidence interval of the true mean. if a day care center were starting up and wanted to keep tuition low, what would be a reasonable amount to charge?

round answers to whole numbers. write confidence interval using $ sign as an ordered pair with space after the comma.\na random sample of 50 four - year - olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. find the 90% confidence interval of the true mean. if a day care center were starting up and wanted to keep tuition low, what would be a reasonable amount to charge?

Answer

Explanation:

Step1: Find the z - score for 90% confidence level

For a 90% confidence level, the significance level (\alpha=1 - 0.90=0.10), and (\alpha/2 = 0.05). The z - score (z_{\alpha/2}) corresponding to the area of (1-\alpha/2 = 0.95) in the standard normal distribution is (z_{0.05}\approx1.645) (from standard normal table).

Step2: Calculate the margin of error (E)

The formula for the margin of error when the population standard deviation (\sigma) is known is (E = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}). Given (n = 50), (\sigma=630), (z_{\alpha/2}=1.645) (E=1.645\times\frac{630}{\sqrt{50}}) First, (\sqrt{50}\approx7.071) (E = 1.645\times\frac{630}{7.071}) (\frac{630}{7.071}\approx89.1) (E=1.645\times89.1\approx146.6)

Step3: Calculate the confidence interval

The confidence interval for the population mean (\mu) is given by (\bar{x}-E<\mu <\bar{x} + E) Given (\bar{x}=3987) (\bar{x}-E=3987- 146.6=3840.4\approx3840) (\bar{x}+E=3987 + 146.6=4133.6\approx4134)

Answer:

(($3840,$4134))