Minutes
126.53 127.27 130 130.35 130.4 130.58
130.87 131.18 131.98 132.55 133.28 133.42
133.43 133.55 133.65 134 134.37 134.62
134.73 135 135.95 136.12 136.17 136.23
136.28 137.7 137.83 137.93 138.18 138.25
138.43 138.67 139.13 139.72 140.25 140.38
140.4 140.42 140.5 141.27 141.3 141.85
141.95 142.72 143.15 143.33 143.4 143.78
143.9 143.95 144.13 144.32 144.47 144.8
145.05 145.18 145.83 146.48 146.92 147.28
148.07 148.23 148.43 148.67 149.08 149.47
149.62 149.92 150.12 150.43 151.72 152.58
153.53 155.1 159.02 161.13 Use the Sampling Distribution for a Mean option in StatKey to create a sampling distribution using samples of size n equals 10 from Table 1 showing the number of minutes to finish the marathon at the Olympics. Generate at least 1000 samples in your sampling distribution and give the standard error of the sample means. need to understand how to solve thanks
To create a sampling distribution using samples of size n equals 10 from the given data, you can follow these steps using StatKey:
1. Go to the StatKey website: https://www.lock5stat.com/StatKey/sampling_distributions/sampling_distributions.html
2. In the "Populations available" section, select the "User-Entered" option.
3. Copy and paste the given data (the marathon finish times) into the "Data input" section.
4. Click on the "Statistics" tab.
5. In the "Sample size" box, enter "10" since you want to create samples of size 10.
6. In the "Number of Samples" box, enter a number greater than or equal to 1000 to generate at least 1000 samples. For example, you can enter "1000" or "2000".
7. Click on the "Generate Samples" button.
8. Once the sampling distribution is generated, you will see the mean and standard deviation of the sample means displayed in the table.
The standard error of the sample means can be calculated by dividing the standard deviation of the sample means by the square root of the sample size (10 in this case). The standard error will give you an estimate of how much the sample mean might differ from the population mean.
Note: Since StatKey is an online tool, you need to have access to the internet to use it.
To solve this problem, you can use the Sampling Distribution for a Mean option in StatKey, which will allow you to create a sampling distribution using samples of size 10 from the given data. Here's a step-by-step guide on how to solve this:
1. Input the given data into StatKey. The data represents the number of minutes to finish the marathon at the Olympics.
2. Select the Sampling Distribution for a Mean option in StatKey. This option will generate a sampling distribution of the sample means.
3. Specify the sample size (n), which in this case is 10. This means that each sample in the sampling distribution will consist of 10 marathon finishing times.
4. Set the number of samples to generate. You need to generate at least 1000 samples to obtain an accurate sampling distribution.
5. Once you have generated the sampling distribution in StatKey, look for the standard error of the sample means. The standard error measures the variability of the sample means in the sampling distribution and is an indicator of the accuracy of the estimate of the population mean.
By following these steps, you will be able to obtain the sampling distribution using samples of size 10 from the given data, and find the standard error of the sample means.