Mathematics, 30.03.2020 21:41 rcmhargoux2970

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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Answer from: Aristar

$t=\frac{2.1-2}{\frac{0.3}{\sqrt{35}}}=1.972$

$p_v =P(t_{34}1.972)=0.0284$

If we compare the p value and the significance level given $\alpha=0.05$ we see that p_v 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

$\bar X=2.1$ represent the sample mean

s=0.3 represent the sample standard deviation

n=35 sample size

$\mu_o =2$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

p_v represent the p value for the test (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: $\mu \leq 2$

Alternative hypothesis: $\mu 2$

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:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

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:

$t=\frac{2.1-2}{\frac{0.3}{\sqrt{35}}}=1.972$

P-value

We calculate the degrees of freedom given by:

df = n-1 = 35-1 = 34

Since is a right tailed test the p value would be:

$p_v =P(t_{34}1.972)=0.0284$

Conclusion

Answer from: Quest

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

Answer from: Quest

Dwould be the answer

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