Question

Calculate the standard error of a sample mean.

The daily high temperatures, in degrees Fahrenheit, of Des Moines for one week were:

Day Temperature (in Fahrenheit)
Monday 64.5
Tuesday 64
Wednesday 66.5
Thursday 64
Friday 62.5
Saturday 61
Sunday 63

Using the data above, what is the standard error of the sample mean? Answer choices are rounded to the hundredths place.

Answer 1

Answer is 0.66, have a good day

Answer 2

The standard error of the sample mean is approximately

0.66 degrees Fahrenheit.

Explanation:

First, we need to calculate the sample mean:

(64.5 + 64 + 66.5 + 64 + 62.5 + 61 + 63) / 7 = 63.5

Next, we need to calculate the standard deviation of the sample:

Step 1: Calculate the variance

- Calculate the difference between each temperature reading and the sample mean:

64.5 - 63.5 = 1

64 - 63.5 = 0.5

66.5 - 63.5 = 3

64 - 63.5 = 0.5

62.5 - 63.5 = -1

61 - 63.5 = -2.5

63 - 63.5 = -0.5

- Square each difference:

1^2 = 1

0.5^2 = 0.25

3^2 = 9

0.5^2 = 0.25

(-1)^2 = 1

(-2.5)^2 = 6.25

(-0.5)^2 = 0.25

- Add up the squared differences:

1 + 0.25 + 9 + 0.25 + 1 + 6.25 + 0.25 = 18.25

- Divide by the sample size (n-1):

18.25 / 6 = 3.04

Step 2: Calculate the standard deviation

- Take the square root of the variance:

√3.04 ≈ 1.74

Finally, we can calculate the standard error of the sample mean by dividing the standard deviation by the square root of the sample size:

1.74 / √7 ≈ 0.66