HO: μ > 5
H1: μ = 5
Where,
μ = the population mean number of times children in your city make trips to a store
- Explain the meaning of the Type I and Type II errors in the context of this scenario. (3 points)
A Type I error occurs when the null hypothesis is correct but the significance value indicates that it should be rejected. In this case, if the actual mean number of times children in your city make trips to a store is greater than 5 and we reject the null hypothesis, a type I error will have occurred.
A type II error occurs when the null hypothesis is incorrect by the significance value indicates that it should not be rejected. In this case, if the actual mean number of times children in your city make trips to a store is less than 5 and we fail to reject the null hypothesis, a type II error will have occurred.
- Suppose that you carry out a similar study in the city in which you live. You take a sample of 100 children and find that the mean number of trips to the store is 5.47 and the sample standard deviation of the number of trips to the store is 1.6. At the 0.01 level of significance, is there evidence that the population mean number of trips to the store is greater than 5 per week? (5 points)
In order to find p-value, we convert this into a z score.
Z-score = (x - μ) / Standard Deviation
Where,
x = 5.47
μ = 5
Standard Deviation = 1.6
= (5.47 - 5) / 1.6
= 0.29375
The p-Value is for this Z score is 0.384494.
- Interpret the meaning of the p-value in C. (10 points)
The p value calculated above is 0.384494 this indicates that we should not reject the null hypothesis at 0.01 significance level. This indicates that at the 0.01 level of significance there is evidence that the population mean number of trips to the store is greater than 5 per week. This indicates that the result is significant at p < 0.01.
References
Barlow, R. (2007). Statistics: A guide to the use of statistical methods in physical sciences. Chichester: Wiley.
Wasserman, L. (2004). All of statistics: A concise course in statistical inference. New York: Springer.
