True or False
If a sample of at least 30 scores is randomly selected from a normal population, the sample mean will be equal to the population mean.
False. Should read "...the sampling distribution of the mean will be equal to the population mean." (Central Limit Theorem)
True
True.
When a sample is randomly selected from a normal population, it is expected that the sample mean will be very close to the population mean. This is due to the Central Limit Theorem, which states that as sample size increases, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution.
In the case of a sample size of at least 30, the sample mean is likely to be a good estimate of the population mean because the larger the sample size, the more representative it is of the entire population. While it is possible for the sample mean to be slightly different from the population mean due to random sampling variability, it is expected to be very close in most cases.
To determine whether the sample mean is equal to the population mean, you would need to calculate the sample mean using the formula:
Sample Mean = Sum of all scores in the sample / Number of scores in the sample
Compare the calculated sample mean to the known population mean to determine if they are equal.