Question

Question 3: Hypothesis Testing - One-Sided Test Boston Co. Cereal, Inc., has asked you to study the variability of the weights of cereal bags produced in their plant located in rural Indonesia. The package weights are known to be normally distributed with the variance of 50. Using a random sample of n=71, you find that the sample mean weight is 40. The marketing vice president claims that there is a very small chance that the population means weight is less than 39.

a. Use an appropriate statistical analysis at 10% level of significance (hypothesis testing) to evaluate his claim. After the test has been conducted, what can you say about his claim?

b. What is the p-value of your test? Explain and include a diagram.

Answer 1

We will use z statistic

H0 :The population means weight is 39.

H1: The population means weight is less than 39.

Test statistic:

Level of significance  α =.10

Test criteria

Reject H0 if calulated Z is less than -Z_α

Calculation

n= 71

σ²= 50

σ= 7.071067

x̅= 40

μ₀ = 39

Z score =

Calculated Z ​=−1.28

Conclusion

Since it is observed that z = 1.192 >-1.28, it is then concluded that the null hypothesis is not rejected.

and conclude that mean weight is 39.

Part b

The p-value is p = 0.8833

Using the P-value approach: The p-value is p = 0.8833, and since 0.8833≥.10, it is concluded that the null hypothesis is not rejected.