The smaller the SEM the larger the mean the smaller the valu

The smaller the SEM,

the larger the mean

the smaller the value of the test statistic

the more confidence we have that the estimates from the sample include the population value

the less confidence we have that the estimates from the sample include the population value

Solution

The smaller the SEM,

the larger the mean

the smaller the value of the test statistic

the more confidence we have that the estimates from the sample include the population value

the less confidence we have that the estimates from the sample include the population value

The standard error decreases with increasing sample size. The standard deviation is most often used to refer to the individual observations. So standard deviation describes the variability of the individual observations while standard error shows the variability of the estimator. When their standard error decreases to 0 as the sample size increases the estimators are consistent.