Math Questions

The z test is a statistical test for the mean of a population. It can be used when n≥30, or when the population is normally distributed and σ is known.

The formula for the z-test is

Z= =

Where

Xbar= sample mean

μ=hypothesized population mean

σ=population standard deviation

n=sample size

The P-values for the z-test can be found by using the standard normal distribution table(refer the following link, scroll down for the table).First find the area under the standard normal distribution curve corresponding to the z test value, then subtract this area from .5000 to get the P-value for a right-tailed or a left-tailed test. To get the P- value for a two-tailed test, double this area after subtracting.

http://en.wikipedia.org/wiki/Standard_normal_table#Normal_and_standard_normal_distribution

You can find the table and some examples, as you refer the link above.

When 95% confidence interval (5% significance level) is to be found, α=0.05.

When 99% confidence interval (1% significance level) is to be found, α=0.01.

When 90% confidence interval (10% significance level) is to be found, α=.10.

To draw the conclusion, if P-value is less than α, reject the null hypothesis. If the P-value is greater than α, do not reject the null hypothesis.

Note that small p-values will result in a rejection of Null hypothesis and large P-values will result in failing to reject Null hypothesis.

#6 is a two tailed test , Ho: μ =6 and H1 : μ ≠ 6 .

You do not need t-test in any of the problems in this assignment.

The t-test is a statistical test for the mean of a population and is used when the population is normally or approximately distributed, σ is unknown and n < 30.

The formula for t test is t=

The degrees of freedom are d.f=n-1.

To find the critical t value at the specified significant level, you have to refer t-distribution table.