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
tatuchka [14]
3 years ago
11

5) In a certain supermarket, a sample of 60 customers who used a self-service checkout lane averaged 5.2 minutes of checkout tim

e, with a standard deviation of 3.1 minutes. A sample of 72 customers who used a cashier averaged 6.1 minutes with a standard deviation of 2.8 minutes. Suppose it is reasonable to assume that the two variance of the two groups are the same. Can you conclude that the mean checkout time is less for people who use the self-service lane
Mathematics
1 answer:
Ne4ueva [31]3 years ago
5 0

Answer:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

S_p=2.940

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

df=60+72-2=130

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

Step-by-step explanation:

Data given

Our notation on this case :

n_1 =60 represent the sample size for people who used a self service

n_2 =72 represent the sample size for people who used a cashier

\bar X_1 =5.2 represent the sample mean for people who used a self service

\bar X_2 =6.1 represent the sample mean people who used a cashier

s_1=3.1 represent the sample standard deviation for people who used a self service

s_2=2.8 represent the sample standard deviation for people who used a cashier

Assumptions

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\sigma^2_1 =\sigma^2_2 =\sigma^2

The statistic is given by:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

And t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

System of hypothesis

Null hypothesis: \mu_1 \geq \mu_2

Alternative hypothesis: \mu_1 < \mu_2

This system is equivalent to:

Null hypothesis: \mu_1 - \mu_2 \geq 0

Alternative hypothesis: \mu_1 -\mu_2 < 0

We can find the pooled variance:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

And the deviation would be just the square root of the variance:

S_p=2.940

The statistic is given by:

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

The degrees of freedom are given by:

df=60+72-2=130

And now we can calculate the p value with:

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

You might be interested in
The Chimera Ant population is 7,500 and grows 3% each year. What will the population be after 3 years.
Mashutka [201]
8175 because the 3 percent of 3 years is 675
8 0
3 years ago
Please help me solve “Expand log3 4x”
castortr0y [4]

Answer:

Look below.

Step-by-step explanation:

Log3^4x

4xLog3 ------> To expand you would take the exponent and put infront of Log

This is the answer if its expanded. The question was sort of scarce so if this is wrong im sorry.

4 0
2 years ago
Create an equation in point slope form of the following graph.
blondinia [14]

Answer:

jus sad u need to start paying attenion to class but the anwser is nun of yp bu

Step-by-step explanation:

4 0
3 years ago
Tammy's allowance is $5.00. She did extra chores around the house and earned an
ikadub [295]

Answer:

5.50 this should help :p

8 0
3 years ago
Read 2 more answers
PLEASE HELP ! WILL MARK BRAINLIEST !You have seven red marbles and seven blue marbles in a bag. You randomly take a marble from
katrin2010 [14]

Answer:

P= 3/13

Step-by-step explanation:

R=7

B=7

Total=14

P(one red marble)=7/14=1/2

P(another red marble no replacement)=6/13

1/2 times 6/13=6/26=3/13

6 0
3 years ago
Read 2 more answers
Other questions:
  • 4x10+(8x1/10)+(2x1/1000) in standard Form
    7·1 answer
  • Please Help Quickly!
    5·2 answers
  • Solve for x. <br><br> −1/3x≤−6
    12·1 answer
  • the four highest scores on the floor exercise at a gymnastics meet were 9.675 9.25 9.325 and 9.5 points. choose the numbers that
    13·1 answer
  • What does it mean to have like square roots?
    14·1 answer
  • How do you make 8 out of 8, 12, 2, 7, 4
    5·1 answer
  • Please help and give brainliest answer
    8·1 answer
  • What will be the first negative term in the sequence 87,84,81​
    12·1 answer
  • What is the range of fat grams for the five sandwiches
    10·1 answer
  • The sum of two consecutive integers is 75.<br> What is the first number?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!