Question

"Hot Tamales" are chewy, cinnamon flavored candies. A bulk vending machine is known to dispense, on average, 15 Hot Tamales per bag. A student chose to test that claim by randomly obtaining 150 bags of Hot Tan1ales and counting the number of candies per bag. The sample mean number of candies was 15.4 with a standard deviation of 0.7.

A.) To test whether the true mean of candies dispensed is different than the vending machine claim, state the null and alternative hypothesis.

B.) What is the critical z-value for this problem?

C.) What is the p-value (observed significance) for this problem?

D.) At the .05 level of significance, what is your conclusion? Explain how you know…

E.) What is the probability of "alpha error" for this problem?

Answer 1

A) Null hypothesis: The Population mean is 15. ()

Vs

Alternative Hypothesis: The population mean is not equal to 15

B) Given,

  

We used Z-test to test the null hypothesis:

Here Zcrit = 1.96 at 5% level of significance.

C) Here the P value by using the calculator is p=0.0001

D) Conclusion Here Pvalue =0.0001 is less than 0.05 hence we reject the null hypothesis at 5% level of significance. Hence the population mean is different than 15.

E) Here the Probability of "alpha error" is 0.05.