Question

Business majors at SU over the past several years have spent a mean of 95 minutes each day studying economics.   A random sample of 30 freshman Business majors were asked how long they studied economics and their response was a mean of 90 minutes with a standard deviation of 9.4

Determine whether freshman spend less time studying economics.

Check assumptions:

Hypotheses:      Ho:                        Ha:

Test Statistic:       P-value:

Conclusion: (reject or fail to reject Ho and interpret to problem)

Answer 1

Given data

population mean

Sample size taken (n)=30

Sample mean

Sample standard daviation

here the claim is wheather the mean time is less or not so our hypothesis will be

Now for Test statistic as the sample size is =30 so we will perform a Z test so from the formula we have test statistic

Now for probablity

As the Z score is negative so it is a lower tail test .so From the standard probablity distribution table for Z score we have probablity value for Z= -2.91 is

P=0.0018

Now conclusion

here confidence level is not given lets chek it for 99% level we have

As we got the p value is too small so we can conclude that

so we can say that the Z will lie on criticle region so we can say that

we have enough evidance to reject the null hypothesis in all confidence level