# hypothesis and standardized test statistic

• Apr 30th 2011, 07:23 AM
njkid110
hypothesis and standardized test statistic
had to miss my stat class the other day and i'm having trouble on my homework. i got a little but any step by step guidance would be appreciated

The Department of Economic and Community Development (DECD) reported that in 2009 the
average number of new jobs created per county was 450. The department also provided the following
information regarding a sample of 5 counties in 2010.
County New Jobs Created
In 2010
Rhea 480
Marion 407
Grundy 428
Sequatchie 400
a. Compute the sample average and the standard deviation for 2010.
b. We want to determine whether there has been a significant decrease in the average number
of jobs created. Provide the null and the alternative hypotheses.
c. Compute the standardized test statistic. Assume the population is normally distributed.
d. At 5% (α = .05) significance, test the hypotheses. State your conclusion.

a) mean = 410 + 480 +407 + 428 + 400 / 5

Deviation = sqrt[(410-425)^2 + (480-425)^2 + (407-425)^2 + (428-425)^2 + (400-425)^2 / 4]

= 32.43

...and i'm lost now
• May 7th 2011, 08:26 AM
mcp2
Your standard deviation and thus your variance is incorrect, what you're looking for is an unbiased estimate of the variance for the population. Take a look through here and I'll help you further, Unbiased and Biased Estimators
• May 8th 2011, 12:48 AM
amul28
why should it be denominator $n$ not $(n-1)$.
• May 8th 2011, 02:15 AM
mcp2
Quote:

Originally Posted by amul28
why should it be denominator $n$ not $(n-1)$.

When working out the variance from a sample, it is usually smaller than the variance of the population, so we divide by $(n-1)$ so that it is a larger number and closer to the actual variance.
• May 8th 2011, 03:15 AM
amul28
I agree hat you said is correct but what njkid110 did also seems correct for me.
I don't get where i am lost.