1. A consumer products company is formulating a new shampoo and is interested in
ID: 3311253 • Letter: 1
Question
1. A consumer products company is formulating a new shampoo and is interested in foam height (measured in mm). Assume that foam height is normally distributed with a standard deviatioin 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 3] a=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 consequences (specific to the context of this problem) of such an error? 13Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 175
Alternative hypothesis: > 175
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
zcritical = 1.645
We will reject the null hypothesis if z-value is greater than 1.645.
b)
Thus the P-value in this analysis is 0.043.
Interpret results. Since the P-value (0.043) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that mean foam height exceeds 175 cm.
There can be type I error.
In this type I error, may be null hypothesis is true, we are wrongly accepting the claim that mean foam height exceeds 175 cm.
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