1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sergeinik [125]
3 years ago
14

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

8 cereal bars of thisbrand, the saturated fat content was 0.6, 0.7, 0.7, 0.3,0.4, 0.5, 0.4, and 0.2. Would you agree with the claim?Assume a normal distribution.
Mathematics
2 answers:
finlep [7]3 years ago
4 0

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

gavmur [86]3 years ago
4 0

Answer:

Yes, it is actually

Step-by-step explanation:

You might be interested in
Determine the domain of the function.
nydimaria [60]
f(x)=\dfrac{4}{x^2}D:\ x^2\neq0\to x\neq0\\\\Answer:\ All\ real\ numbers\ except\ 0.
6 0
3 years ago
The variables y and x have a proportional relationship, and y = 25 when x = 60.
jeka94

Answer:

A

Step-by-step explanation:

A. x = 25

4 0
3 years ago
Read 2 more answers
Why do you rarely find math teachers spending time at the beach
Sliva [168]

They are busy grading papers and preparing for other things.

8 0
3 years ago
Triangle PQR has coordinates P(–8, 3), Q(–8, 6), and R(–3, 6). If the triangle is translated by using the rule (x, y) right-arro
amid [387]

Answer:

Step-by-step explanation: in the x's place add 4 to that number and in the y's place subtract 6 from that number:

P= -4,-3

Q= -4,0

R= 1, 0

3 0
3 years ago
Read 2 more answers
Which expression is equivalent to the one below?<br> (26 x 96) = 1814
vfiekz [6]

Answer:

the answer is A.

Step-by-step explanation:

(2^{6}×9^{6})÷18^{14}

2×9= 18

6+6= 12

18^{12}÷18^{14}

18^{12-14}= 18^{-2}

1/18^{-2}

3 0
2 years ago
Other questions:
  • 2/7 (x +4) = 6 solve for x​
    9·2 answers
  • Use breaking apart to find the product for 9 ×36
    7·1 answer
  • BRAINLIEST ASAP! PLEASE. HELP ME :) I need help with part 2 of the question.
    12·2 answers
  • 1/4 and 1 1/2 times as much
    9·1 answer
  • If f(1) = 1 and f(n) = 3f(n − 1) then find the value of f (6).​
    9·1 answer
  • The band will play for 60 minutes. If the members want to play 5 equal length, how many seconds will each song have to be?​
    5·1 answer
  • Help I will give brainliest
    14·2 answers
  • If the width of the cereal box was 4 instead of 2, what would be the surface area?
    11·2 answers
  • Kala invested $8000 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment w
    6·2 answers
  • Which values are in the solution set of the compound inequality? Select two options
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!