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KarenH3512
30.03.2020 •
Mathematics
Suppose the food label on a cookie bag states that there is at most 2 grams of saturated fat in a single cookie. In a sample of 35 cookies, it is found that the mean amount of saturated fat per cookie is 2.1 grams. Assume that the sample standard deviation is 0.3 gram. At 0.05 significance level, can we reject the claim on food label
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Ответ:
If we compare the p value and the significance level given
we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 2 at 5% of signficance.
Step-by-step explanation:
Data given and notation
z would represent the statistic (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is at least 2 grams, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
We calculate the degrees of freedom given by:
Since is a right tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given
we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 2 at 5% of signficance.
Ответ: