Help with Statistics!?

To test this, we must use a hypothesis test using a t distribution, since we are dealing with a sample standard deviation. With, a significance level of 0.05 and a sample size of 100, the critical value for t will equal +/-1.99. Our test stat is our sample mean minus population mean all divided by the standard deviation over the square root of n, our sample size [(493-500)/(32/sq.rt.100)]. This gives us -7 divided by 3.2, which then gives us -2.188. Because our test statistic is outside of our critical value of -1.99, we can conclude that there is a statistical difference between the sample mean and the population mean. In essence, yes the manufacturer is misleading.