A random sample of 250 households in a large city revealed that the mean number of televisions per household was 2.76. From previous analyses we know that the population Std Dev. is 1.8. Can we conclude at the 5% significance level that the true mean number of television per household is at least 2.5?
2007-04-08 01:56:05 · 4 answers · asked by mj D 1 in Science & Mathematics ➔ Mathematics
Hi,
At the 5% significance level, that means 95% of results should be in the acceptable range. That means 45% below the mean and the 50% above the mean are all acceptable Z scores. The z-score to represent 45% below the mean is -1.645.
When you take the formula
z = (x value - mean)/( std. dev. /sqrt(n)), and fill it in, you get
z = (2.5-2.76)/(1.8/sqrt(250)) = -2.28 as your Z score. Since that is more than 1.645 below the mean, you can not conclude that the true mean number is at least 2.5 at a 5% significance level.
I hope that helps!! :-)
2007-04-08 02:15:52 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
Are you finding solution to some assignment of any university?
Any how, we can conclude that the true mean is at least 2.5.
2007-04-08 09:03:37 · answer #2 · answered by ranjeevtyagi 1 · 0⤊ 0⤋
Yes.
2007-04-08 09:03:12 · answer #3 · answered by ag_iitkgp 7 · 0⤊ 0⤋
That sounds about right
2007-04-08 09:01:09 · answer #4 · answered by Carolyn D 1 · 0⤊ 1⤋