Statistics Questions: Z-Value and Level of Significance?

I'm going to explain it to you z-scores and lvl of sign. as easy as possible please give me 10 points :). A z-score means how far a number is from the sample mean in terms of standard deviations. For ex: let's take the numbers 4 & 6. The mean is 5 obviously since 4+6=10 10/2=5. If they told us to find the calculated z-value for 5 the answer would be 0 because 0 is how many standard deviations our 5 is from the mean 5. for 20 the z-score would 3 since that is how many stan. dev. it's from 5. So basically the closer your number's z-score is to 0 the closer you are to your mean and the farther away your number's z-score is to 0 the farther away you are from the mean.

The lvl of sign is used to determine whether or not you can accept you null hypothesis. You have to look at your pvalue. so in this case our lvl of sign is .01 which means that if our p value ends out being >=.01 we reject but if it is <.01 we accept the null hypothesis. In your problem the p-value is going to be much, much less than .01 so you will reject the null hypothesis. Hope this helps.

1) For both a 2-tail and 1-tail test the p-value should be <0.01 since

P(Z>=4.6) <0.00003.

2) The z-value would be negative for the alternative to be mu<5 and it is not.

3) The null is almost certainly to be rejected since the p-value is so small.

4)This is correct, see above.

If you look at the z-table you find that the values are given for -3.8<z<3.8, with p-values very close to zero (0.0000) to 0.9999.

If your test is one-tailed right -critical region is of the form {Z>z}, then

P{Z>4.6} is certainly < 0.01.

If your test is two-tailed -critical region is of the form {|Z|>z}, then

P{|Z|>4.6} = 2*P{Z>z} is also certainly < 0.01.

The p-value is likely to be less than 0.01? Certainly, in fact

The null hypothesis will most likely be rejected? Will certainly ...

in case you be conscious z-table is tabulated for -3.80<z<3.8, at left end P is amazingly a lot on the point of 0, at the different aspect very on the point of one million. With z=4.6 i'd bypass for The p-value is really decrease than 0.01 The null hypothesis is of direction rejected.