Question

Weights, in pounds, of ten-year-old girls are collected from a neighborhood. A sample of 26 is given below. Assuming normality, use Excel to find the 98% confidence interval for the population mean weight μ. Round your answers to three decimal places and use increasing order.

66.4
86.3
71.3
52.8
68.0
85.0
66.2
79.2
93.5
84.5
71.1
74.5
65.0
58.5
59.8
80.2
69.2
92.9
78.9
59.4
63.6
66.5
60.7
80.1
60.4
74.5

Answer 1

The 98% confidence interval for the sample mean is (66.763, 76.969).

The primary challenge with this topic is entering all of the data into an Excel spreadsheet. After completing this step, the issue is not tough. Here, we're going to assume that the standard deviation is unknown. It's also important to note that the data was written from cell A1 to cell A26.

let's figure out what the sample mean is. The Excel function AVERAGE can be used to do this. To enter the mean value in cell B1, first mark the cell and enter =AVERAGE(A1:A26). You'll see that the function's arguments are our data's first and last cell. After rounding, we obtain μ = 71.86538462 and μ = 71.866.

Since we do not yet know the theoretical standard deviation, we must now compute the sample standard deviation. The Excel function STDEV can be used for this. To enter the mean value in cell B2, first mark the cell and enter =STDEV(A1:A26). You'll see that the function's arguments are our data's first and last cell.

This gives us σ = 11.0160226 and, after rounding, σ = 11.016.

We intend to compute the degree of confidence. CONFIDENCE is an Excel function that can be used for this. In cell B3, we mark the cell and enter =CONFIDENCE(0.02;11.016;26) if we wish to write the mean. Let's clarify what the arguments of the CONFIDENCE function are:

The confidence level is expressed as a number, 0.02. As you can see, the problem description required us to determine "the 98% confidence interval." However, since Excel is unable to interpret this data, we must "normalise" it by applying the calculation

1 - 98/100 = 1-0.98=0.02.

The standard deviation found in the second step is represented by the second value, 11.016.

This gives us ε=5,10298125 for the confidence and ε=5,103 for the rounding.

Lastly, we will determine the confidence interval. The outcomes of the first and third steps will be used in this instance. The formula (μ - ε, μ + ε) yields the confidence interval. Next,

(μ - ε, μ + ε) = (71.866 - 5,103, 71.866 + 5,103) = (66.763, 76.969)

Answer 2

The 98% confidence interval for the sample mean is (66.763, 76.969).

Explanation:

The main difficulty of this problem is to write all the data into an Excel sheet. Once we have done this part the problem is not difficult. Here we are assuming that we do not know the standard deviation. Also, we need to remark that the data has been written from the cell A1 to the cell A26.

First step: Let us calculate the mean of the sample. This can be done using an Excel function: AVERAGE. If we want to write the mean in the cell B1, we mark the cell and then write =AVERAGE(A1:A26). Notice that the arguments of the function is the first and the last cell of our data. With this we get that μ = 71.86538462 , and rounding μ = 71.866.

Second step: Now we need to calculate the standard deviation of the sample, because we do not know the theoretical standard deviation. This can be done using an Excel function: STDEV. If we want to write the mean in the cell B2, we mark the cell and then write =STDEV(A1:A26). Notice that the arguments of the function is the first and the last cell of our data. With this we get that σ = 11.0160226 and rounding σ = 11.016.

Third step: We are going to calculate the confidence. This can be done using an Excel function: CONFIDENCE. If we want to write the mean in the cell B3, we mark the cell and then write =CONFIDENCE(0.02;11.016;26). Let us explain what are the arguments of the function CONFIDENCE:

• The number 0.02 is the level of confidence. Notice that in the statement of the problem we were asked to find ‘‘the 98% confidence interval’’, but Excel can not understand this data, so we need to ‘‘normalize’’ it using the formula 1 - 98/100 = 1-0.98=0.02.

• The second number, 11.016, is the standard deviation obtained in the second step.

• The 26 is the number of samples we have.

With this we get that the confidence is ε=5,10298125 , and rounding is ε=5,103.

Fourth step: Finally we are going to find the confidence interval. Here we are going to use the results of the first and third step. The confidence interval is obtained by the formula (μ - ε, μ + ε). Then,

(μ - ε, μ + ε) = (71.866 - 5,103, 71.866 + 5,103) = (66.763, 76.969)