Final answer:
To find the 95% confidence interval for the population mean, we can use the sample mean, standard deviation, and sample size. Using the formula, we can calculate the lower and upper bounds of the confidence interval. The 95% confidence interval for the population mean is 60.5°F to 64.7°F.
Step-by-step explanation:
To find the 95% confidence interval for the population mean, we can use the formula:
Confidence Interval = sample mean ± (critical value) × (standard deviation / square root of sample size)
In this case, the sample mean is given as , the standard deviation is , and the sample size is 30. To find the critical value, we need to determine the degrees of freedom. Since we have a sample size of 30, we have 29 degrees of freedom. Looking up this value in a t-table or using a calculator, the critical value for a 95% confidence interval is approximately 2.045.
Plugging in the values, we get:
Confidence Interval = 62.5°F ± (2.045) × (2.1°F / )
Calculating the lower and upper bounds of the confidence interval:
Lower bound = 62.5°F - (2.045) × (2.1°F / ) = 60.5°F
Upper bound = 62.5°F + (2.045) × (2.1°F / ) = 64.7°F
Rounding these values to one decimal place, we get the 95% confidence interval for the population mean as 60.5°F to 64.7°F.