![]() That would give us a standard deviation for the sampling distribution of the sample mean. Since the answer to what we are asking comes from the sampling distribution of the sample mean, we would find the appropriate standard deviation to use by dividing the population standard deviation by the square root of the sample size (since the variance of the sampling distribution is the population variance divided by the sample size, and the standard deviation is the square root of the variance). ![]() To use a z-table, we'll need to find the appropriate z-score first. (We could also use a t-table, but it is allowable to just use a z table since our sample size is larger than 30) So now, we can use the normal cumulative density function or a z-table to find this probability. ![]() Under that assumption, and noting also that we are given that the population is normally distributed (or that we took a sample size of at least 30 ), we can treat the sampling distribution of the sample mean as a normal distribution. The p-value is the probability of a statistic at least as deviant as ours occurring under the assumption that the null hypothesis is true.
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