Standardized test scores for all 425 students at a high school are shown below. Hide and shuffle all of the values. Take a random sample of 28 values from the population. Based on that sample, find the mean and sample standard deviation using a statistics calculator. Using those values, create a 95% confidence interval for the true mean of the population, rounding to the nearest tenth.

Question

Standardized test scores for all 425 students at a high school are shown below. Hide and shuffle all of the values. Take a random sample of 28 values from the population. Based on that sample, find the mean and sample standard deviation using a statistics calculator. Using those values, create a 95% confidence interval for the true mean of the population, rounding to the nearest tenth.

Sum of Samples: 1675 Number of Samples: 28

Answer 1

To find the mean and sample standard deviation using a statistics calculator, follow these steps:

1. Input the sample data into the calculator. In this case, you have a sample of 28 values from the population.

2. Use the calculator's functions to find the mean of the sample. The mean is simply the sum of all the values divided by the number of values. In this case, the sum of the samples is 1675 and the number of samples is 28. So, divide 1675 by 28 to get the mean.

Mean = 1675 / 28 = 59.8214 (rounded to four decimal places)

3. Next, calculate the sample standard deviation using the calculator's functions. The sample standard deviation measures the spread of the data within the sample. It can be calculated by finding the square root of the variance, which is the average of the squared deviations from the mean. The calculator should have a specific function for calculating the sample standard deviation or variance.

4. After finding the sample standard deviation, you can use it to create a 95% confidence interval for the true mean of the population. The formula for the confidence interval is:

CI = mean ± (1.96 * (sample standard deviation / √number of samples))

In this case, the mean is 59.8214 and the sample standard deviation is calculated in step 3. The number of samples is 28. Substitute these values into the formula to calculate the confidence interval.

CI = 59.8214 ± (1.96 * (sample standard deviation / √28))

Note that 1.96 corresponds to a 95% confidence level, as it is a z-value for a 95% confidence interval.

5. Finally, calculate the confidence interval using the values from step 4. Round the final result to the nearest tenth.

Confidence Interval = 59.8214 ± (1.96 * (sample standard deviation / √28))