You need to state the null and alternative hypothesis and state where the claim

Question

You need to state the null and alternative hypothesis and state where the claim is. For the mean of first population use mu1 and for the second population mean use mu2. For propotions. use P1 and P2 to refere to population proportions. You may use your calculator.

For example a null and alternative hypothesis could be
Ho: mu1 = mu2
Ha: mu1 is not equal to mu2

A random sample of 10 travel brochures showed sample mean cost of an 8 day cruise to the Bahamas $1,978. (1st class, double occupancy). The sample standard deviation was $250. An independent random sample of 12 travel brochures showed mean cost of a comparable 8 day cruise to Mexico $2,150 with sample standard deviation $275. Test to see if the population mean costs for the two types of cruises are different. Use a 1% significance level.

Explanation / Answer

The test hypothesis is
Ho:?1=?2
Ha:?1 not equal to?2

The test statisitic is

t=(xbar1-xbar2)/?[s1^2/n1+s2^2/n2]

=(1978-2150)/sqrt(250^2/10+275^2/12)

=-1.54

Given a=0.01, the critical value is t(0.005,df=n1+n2-2=20)=-2.85 (check student t table)

Since -1.54 is larger than -2.85, we do not reject Ho.

So we can not conclude that the population mean costs for the two types of cruises are different.

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