Problems of chapter 9 of statistics

Question

A box of chocolates should weigh 16.4 ounces. A sample of 40 randomly selected boxes had a mean weight of 16.6 ounces, with a standard deviation of 0.4 ounces. At a 0.05 significance level, test the claim that the mean weight of these boxes is greater than 16.4 ounces.

 

 

1) State the null and alternative hypotheses

A)        B)   

C)       D)   

Answer A, B, C, or D in the box

Ho: 

H1: 

2) Compute test statistics. Round the answer to two decimal places.

test statistics = 

3) Compute the P value. Round your answer to four decimal places.

P value = 

4) Compute the critical value. Round your answer to four decimal places. 

 critical value = 

5) Decision

E) Reject the Ho

F) Do not reject the Ho

Type E or F in the box 

6) Conclusion

G) There is enough evidence to support the claim that the mean of boxes is greater than 16.4 ounces.

H) There is not enough evidence to support the claim that the mean of boxes is greater than 16.4 ounces. 

Answer 1

Ho: mu = 16.4

Ha: mu > 16.4

test statistic t = (sample mean - 16.4)/(standard deviation/square root(sample size)

= (16.6 - 16.4)/(0.4/sqrt(40)) = 3.16

degrees of freedom = 39

p-value = P(t > 3.16) with 39 DOF = 0.0015

critical value at alpha = 0.05, is t-score for 0.05 tail probability and 39 DOF ~ 1.684

reject Ho

G) There is enough evidence to support the claim that the mean of boxes is greater than 16.4 ounces.