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# Testing of hypothesis: Students t test

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1. A sample of 64 observations is selected from a normal population. The sample mean is 215, and the sample deviation is 15. Conduct the following test of hypothesis using the .03 significance level.

Ho: µ &#8805; 220
H1: µ<220
a. Is this a one or two tail test?
b. What is the decision rule?
c. What is the value of the test statistic?
d. What is your decision regarding Ho?
e. What is the p-value?

Ho: µ&#8804; 10
H1: µ > 10
a. Is this a one or two tail test?
b. What is the decision rule?
c. What is the value of the test statistic?
d. What is your decision regarding Ho?
e. What is the p-value

2. At the time she was hired as a server at the Grumney Family Resturant. Beth Brigden was told , you can average more than \$80 a day in tips. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was \$84.85, with a standard deviation of \$11.38. At the .01 significance level, can Ms. Brigden conclude that she is earning an average of more than \$80 in tips?

##### Solution Summary

One sample Students t test .The solution contains Null Hypothesis, Alternative Hypothesis, Significance Level, Critical Value, P value. Interpretation of the results are also given.

##### Solution Preview

1. A sample of 64 observations is selected from a normal population. The sample mean is 215, and the sample deviation is 15. Conduct the following test of hypothesis using the .03 significance level.

Ho: µ &#8805; 220
H1: µ<220

a. Is this a one or two tail test?
This is a one tailed t test.
b. What is the decision rule?
Rejection criteria: Reject the null hypothesis, if the test statistic is less than the critical value of t with 63 d.f at 0.03 significance level. The test Statistic is given by
c. What is the value of the test statistic?
Test Statistic t = ...

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