(measured in mm). Assume that foam height is normally distributed with a standar
ID: 3310626 • Letter: #
Question
(measured in mm). Assume that foam height is normally distributed with a standard deviation of 20 mm. The company wishes to make the claim that the mean foam height exceeds 175 mm (the advertised claim of one of its competitors). a) State the appropriate hypotheses to be tested in this situation, and also state the general form of the test statistic to be used and the rejection region if a significance level of =0.05 is used. (b) A random sample of n = 15 foam heights are measured, and a p-value of 0.043 is calculated. State the decision and conclusion of the test. What type of error (Type I or Type II) might have been made in coming to this conclusion? What are some potential consequences (specific to the context of this problem) of such an error?Explanation / Answer
a)
A null hypothesis is a hypothesis that says there is no statistical significance between the two variables. It is usually the hypothesis a researcher or experimenter will try to disprove or discredit. Analternative hypothesis is one that states there is a statistically significant relationship between two variables.
H0: Height doesn't exceed 175mm
H1: Height exceeds 175mm
z statistic will be used.
Rejection region: One tail test
Rejection when z > 1.64
b) n = 15
p = 0.043
When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 andinterpreted in the following way: A small p-value (typically 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
As p < 0.05, null will be rejected.
Conclusion: As null is rejected, there is enough evidence to claim that Height exceeds 175mm.
In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).
We can make a type 2 error here.
Consequences: By making this error we assume that height doesn't exceed 175mm but infact it does exceed 175mm. Thus, company might make a wrong advertiement in that case and lose consumers.
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