Question

If the variance of the water temperature in a lake is 30°, how many days should the researcher select to measure the temperature to estimate the true mean within 4° with 95% confidence? Round the intermediate calculations to two decimal places and round up your final answer to the next whole number

Answer 1

Answer: The number of days would be 7 days.

Step-by-step explanation:

Since we have given that

Variance = 30°

Standard deviation = √30 =  5.47

Mean = 4°

At 95% confidence, z = 1.96

So, number of days that the researcher select to measure the temperature would be

$n=(\dfrac{z\times \sigma}{error})^2\\\\n=(\dfrac{1.96\times 5.42}{4})^2\\\\n=7.053\\\\n=7$

Hence, the number of days would be 7 days.