Question

In a city, 22 coffee shops are randomly selected, and the temperature of the coffee sold at each shop is noted. Use Excel to find the 90% confidence interval for the population mean temperature. Assume the temperatures are approximately normally distributed. Round your answers totwo decimal places and use increasing order. Temperature 151 158 163 155 155 144 140 148 145 146 158 143 152 167 163 147 170 168 176 164

Answer 1

Answer:

The confidence interval is (152.03, 159.77)

Step-by-step explanation:

The formula for calculating the confidence interval for a population mean is given by:

$\bar{x}\pm \frac{z_{\alpha/2}*s}{\sqrt{n}}$

The sample size is actually $n = 20$.

The sample average is $\bar{x}=155.90$.

Using excel to calculate the standard deviation we get $s = 10.52$

The confidence level is $1-\alpha=0.90$ therefore $\alpha=0.10$

We obtain the critical value $z_{\alpha/2}=1.65$

In Excel I calculated the margin error before calculating the confidence interval. The margin error is given by:

$\frac{z_{\alpha/2}*s}{\sqrt{n}}=\frac{1.65*10.52}{\sqrt{20}}=3.87$

Now we can calculate the confidence interval.

$\bar{x}\pm \frac{z_{\alpha/2}*s}{\sqrt{n}}=155.90\pm3.87=(152.03, 159.77)$