2 Points

A maker of a certain brand of low-fat cereal barsclaims that the average saturated fat content is 0.5gram. In a random sample of

finlep [7]

Answer:

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

$p_v =2*P(t_{(7)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=0.475$

The sample deviation calculated $s=0.183$

We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 0.5$

Alternative hypothesis: $\mu \neq 0.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so 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:

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=8-1=7$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(7)}$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

4 0

3 years ago

Read 2 more answers

Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, the value of a particul

OverLord2011 [107]

Based from the data within the given problem, the rate in dollars per year at which the price is increasing is 150*ln(1.65)*1.65^t. I am hoping that this answer has satisfied your query about this specific question, thank you and have a nice day.

5 0

4 years ago

Read 2 more answers

Can someone answer question on my profile. thx :)

Zinaida [17]

There is no question

3 0

3 years ago

Plz help on 1,3,4 thx!

Natalka [10]

1. IQR = Q3 - Q1 = 35 - 20 = 15

A. 15

3. The ages include 20 and 25 so A and C are out, and the ages are between the two ages

B. a >= 20 and a <= 25

4. With the addition of 30, there are now 14 dots. Therefore, the median will be the mean of the 7th and 8th dots from least to greatest on the number line. In this case, it would still be 22.

C. The median would stay the same.

6 0

3 years ago

What is the value of the equation on the picture provided

lorasvet [3.4K]

53Step-by-step explanation:The two angles identified are alternate exterior angles.

4 0

3 years ago