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 description best defines FG¯¯¯¯¯ ?
kogti [31]
The answer is A because say there is point H between F and G the point would be considered summarised by F and G 
8 0
3 years ago
Read 2 more answers
There are 92 students that equals 75 how many students are 100 percent
elena-s [515]

Answer:

122.67 or round it to 123

Step-by-step explanation:

i used the butterfly method.

92/75 = x/100.

i multiplied 92*100=9200

then i divided it with 75.

9200/75=x

so the answer is

x=122 or 123

4 0
2 years ago
Read 2 more answers
What is the measure of anglez in this figure?<br> Enter your answer in the box<br> 430<br> z=
strojnjashka [21]
Answer is 137
180 - 43 = 137
3 0
2 years ago
A right triangle has a leg length of 21 inches and a hypotenuse length of 29 inches. What is the length of the other leg?​
Shalnov [3]

Answer:

20

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

21^2 + b^2 = 29^2

441 + b^2 = 841

Subtract 441 on both sides to get b^2 = 400

Take the square root of both sides to get b = 20

4 0
3 years ago
Can someone help me please I don't understand
iVinArrow [24]
The formula for surface area are 2(LW+LH+WH). If the numbers were being placed in the formula, it will become 2[(9*7)+(9*12)+(12*7)]. 9*7 is 63, 9*12 is 108, 12*7 is 84 and the sum will be 255, and multiply by 2 is 510.
The answer is 510
7 0
3 years ago
Other questions:
  • What is the estimated difference? Round each number to the nearest hundred thousand before finding the difference? 3,661,528 – 1
    6·1 answer
  • What is the equation of the line that is parallel to the line y = 1/3x + 4 and passes through the point (6, 5)?
    12·1 answer
  • How many words is 2-3 pages double spaced?
    14·1 answer
  • NEED HELP ON THIS . THANKS FOR THE HELP
    11·1 answer
  • Help plz plz plz plz plz plz plz
    13·1 answer
  • W+3 3/8=1 5/6 what is the answer
    12·1 answer
  • An estate of $686,000 is left to three siblings. The eldest receives 2 times as much as the youngest. The middle sibling receive
    13·2 answers
  • Original: $30.59<br> Discount:25%<br> New: ?
    8·1 answer
  • Please help!!! I'll mark you as BRAINLIEST and give you 10 points!!!!!
    7·1 answer
  • José put $1,500 into a savings account. He earns 3% interest every year. How much simple interest will he earn at the end of 3 y
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!