Test the claim that the mean GPA of night students is larger than 2.8 at the 0.01 significance level.

Question

The null and alternative hypothesis would be:

H0:u<2.8

H1:u>2.8

right tailed

Based on a sample of 50 people, the sample mean GPA was 2.81 with a standard deviation of 0.05

The test statistic is: Incorrec (to 2 decimals)

The p-value is: Incorre(to 2 decimals)

These are the correct answers:

t=1.4142135623731

p=0.0818

I keep missing by decimals , how to calculate in ti84 or geogebra or by hand?



Answer 1

Hi Cynthya,

For test statistic:

t=(xbar-mu)/SE

xbar=sample mean=2.81

mu=hypothesized population mean=2.8

SE=standard error=s/sqrt(n)

s=sample standard deviation=0.05

n=sample size=50

SE=0.05/sqrt(50)

SE=0.0070710678

t=(2.81-2.8)/0.0070710678

t=1.414213562

Use all decimals in intermediate calculations in order to get exact value for t-test statistic.

Sorry, I don't have an 84 Plus, but for p-value, do you have access to Microsoft Excel? I actually just learned this while helping another student. For right-sided t, type the following formula into Excel:

=T.DIST.RT(t, df)

where df=degrees of freedom

df=n-1

df=49

So you would input:

=T.DIST.RT(1.414213562,49)

This will give you:

p=0.081811 or 0.0818 if rounding to 4 decimals.

I hope this helps.