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
Dmitriy789 [7]
3 years ago
14

The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.7 ent

rees per order. On a particular Saturday afternoon, a random sample of 48 Noodles orders had a mean number of entrees equal to 2.1 with a standard deviation equal to 1.01. At the 2 percent level of significance, does this sample show that the average number of entrees per order was greater than expected?
Mathematics
2 answers:
Ulleksa [173]3 years ago
6 0

Answer:

Yes, this sample show that the average number of entrees per order was greater than expected.

Step-by-step explanation:

We are given that the  number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.7 entrees per order. For this a random sample of 48 Noodles orders had a mean number of entrees equal to 2.1 with a standard deviation equal to 1.01.

We have to test that the average number of entrees per order was greater than expected or not.

Let, Null Hypothesis, H_0 : \mu = 1.7 {means that the average number of entrees per order was same as expected of 1.7 entrees per order}

Alternate Hypothesis, H_1 : \mu > 1.7 {means that the average number of entrees per order was greater than expected of 1.7 entrees per order}

The test statistics that will be used here is One sample t-test statistics;

          T.S. = \frac{Xbar-\mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, Xbar = sample mean number of entrees = 2.1

              s = sample standard deviation = 1.01

              n = sample of Noodles = 48

So, test statistics = \frac{2.1-1.7}{\frac{1.01}{\sqrt{48} } } ~ t_4_7

                            = 2.744

<em>Now, at 2% significance level the critical value of t at 47 degree of freedom in t table is given as 2.148. Since our test statistics is more than the critical value of t which means our test statistics will lie in the rejection region. So, we have sufficient evidence to reject our null hypothesis.</em>

Therefore, we conclude that the average number of entrees per order was greater than expected.

SOVA2 [1]3 years ago
4 0

Answer:

t=\frac{2.1-1.7}{\frac{1.01}{\sqrt{48}}}=2.744    

p_v =P(t_{(47)}>2.744)=0.0043  

If we compare the p value and the significance level given \alpha=0.02 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean is higher than 1,7 entrees per order at 2% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=2.1 represent the mean

s=1.01 represent the sample standard deviation

n=48 sample size  

\mu_o =1.7 represent the value that we want to test

\alpha=0.02 represent the significance level for the hypothesis test.  

t 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 higher than 1.7, the system of hypothesis would be:  

Null hypothesis:\mu \leq 1.7  

Alternative hypothesis:\mu > 1.7  

If we analyze the size for the sample is > 30 but 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{2.1-1.7}{\frac{1.01}{\sqrt{48}}}=2.744    

P-value

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

df=n-1=48-1=47  

Since is a one side test the p value would be:  

p_v =P(t_{(47)}>2.744)=0.0043  

Conclusion  

If we compare the p value and the significance level given \alpha=0.02 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean is higher than 1,7 entrees per order at 2% of signficance.  

You might be interested in
Which of the following is the rational exponent expression of sixth root of f?
MAXImum [283]
The rational exponent expression of sixth root of f is  <span>f to the one sixth power
proof
A^1/n, is called n-th root of A, for all n differ from zero</span>
7 0
3 years ago
Read 2 more answers
Relationship B has a lesser rate than Relationship A. This graph represents
Mashcka [7]
I think the answer is C and D..searched it up
3 0
3 years ago
Read 2 more answers
4p – 3 = 13<br><br><br><br> answer pls
Galina-37 [17]
P = 4

13 + 3 = 16
16/4 = 4

These questions require reverse order, you have to work backwards
For example 4 * P you would do 4/P instead
8 0
3 years ago
Read 2 more answers
Write an algebra expression to represent each scenario:<br><br> “the sum of 6 and y”
Lina20 [59]

Answer:

6+y

Step-by-step explanation:

simple:)

5 0
2 years ago
PLEASE HELP ME!!!<br> Which Choice is equivalent to the product below?
skad [1K]
It’s B

6x3=18
sqrt18 simplifies to sqrt9 x sqrt2
sqrt9 is 3 for 3sqrt2
8 0
3 years ago
Other questions:
  • Determine the center and radius of the following circle equation:
    11·1 answer
  • BRAINLIEST to BEST: Help!
    9·2 answers
  • Can somebody plz help and explain this
    11·2 answers
  • The length of a pen is 5 more than its width.The perimeter is 26 m.Find the length and the width.
    8·2 answers
  • Which of the following is equivalent to (x-3)(x^2-2x-3)
    12·1 answer
  • A baker purchased 10 lb of wheat flour and 13 lb of rye flour for a total cost of $17.40. A second purchase, at the same prices,
    11·1 answer
  • Please, help me with this one! Y= 37,39,51
    8·1 answer
  • The diameter of a Frisbee is 12 in. What is the area of the Frisbee?
    8·2 answers
  • Algebra 1 : ordered pairs kinda dont get it
    13·1 answer
  • line y = x + 2 will be graft on the same coordinate plane to create a system of equations. what is the solution to the system of
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!