An executive member of an ice cream company claimed that its product contained m
ID: 3160196 • Letter: A
Question
An executive member of an ice cream company claimed that its product contained more than 500 calories per pint. To test this claim, 81 containers were randomly chosen and analyzed. The sample result showed that the mean was 509 calories with (population) standard deviation of 27 calories. (a) At alpha = 5%, using the classical approach to test the claim. (2) Using P-value approach to conclude it. 2. An Industrial psychological test inventory called POMS (Profile of Mood States) was given to a sample of 49 first-year business professionals. The result showed that the mean was 10.46 with (population) standard deviation of 7.77. A psychologist suspected that, in general, the first-year business professionals have a mean score on POMS that is different from the national norm of 13. (a) At a=l%, using the classical approach to test the claim, (b) Using P-value approach to conclude it.Explanation / Answer
1.
a)
Formulating the null and alternative hypotheses,
Ho: u <= 500
Ha: u > 500
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Getting the test statistic, as
X = sample mean = 509
uo = hypothesized mean = 500
n = sample size = 81
s = standard deviation = 27
Thus, z = (X - uo) * sqrt(n) / s = 3
As z > 1.645, we reject Ho.
There is significant evidence to claim that the product contains more than 500 claories per pint at 0.05 level. [CONCLUSION]
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b)
Also, the p value is, as this is right tailed,
p = 0.001349898 [ANSWER, P VALUE]
As P < 0.05, we reject Ho.
There is significant evidence to claim that the product contains more than 500 claories per pint at 0.05 level. [CONCLUSION]
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