A physical instructor claims that the mean weight of students in school is greater than 82 kg with standard deviation 20. If a sample of size 81 students is selected with mean weight of 90. The test statistic equals to

The correct answer is z = 3.6

Key Points

• The test statistic is a measure of the difference between the sample mean and the population mean in terms of standard deviations.
• In this case, the test statistic can be calculated as follows:
  • \(z = (sample mean - population mean) / (standard deviation / \sqrt(sample size))\)
  • \(z = (90 - 82) / (20 / \sqrt(81))\)
  • z = 3.6

 Additional Information

• The test statistic is a measure of the difference between the sample mean and the population mean in terms of standard deviations.
• The test statistic is calculated by dividing the difference between the sample mean and the population mean by the standard deviation divided by the square root of the sample size.
• The test statistic can be used to determine the significance of the difference between the sample mean and the population mean.
• If the test statistic is large enough, it can be concluded that the sample mean is significantly different from the population mean.

​ Important Points

• The test statistic
  • It is only meaningful if the sample is a random sample.
  • It assumes that the population is normally distributed.
  • It is only one piece of information used to make inferences about the population mean.
    • Other factors, such as the sample size and the variability of the population, must also be taken into account.