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
PLEASEEEE HELPPP Angle A and angle B are two angles that are complementary. We know angle A measures (x+2)° and Angle B measures
saul85 [17]

Answer:

Step-by-step explanation:

x + 2 + 57 = 90

x + 59 = 90

x = 31°

x + 2 = 33°

3 0
3 years ago
Read 2 more answers
Round 227033 to the nearest ten thousand
Sonbull [250]

I a pretty sure it is 228,000 but i am not sure.

7 0
3 years ago
Read 2 more answers
What is the box-and-whiskers plot used to show?
12345 [234]
The whole idea of that kind of graph is that they allow you to view the complete distribution of data while also being able to see first and third quartiles, the median, and the minimums and maximums. 
5 0
2 years ago
What is the surface area of a triangular pyramid if each face has an area of 30 mm2?
coldgirl [10]
The answer must be 120\quad m{ m }^{ 2 } since the triangular pyramid has 4 faces and each has an area of 30 m{ m }^{ 2 } we should multiply that by 4 , so :

4\cdot 30\quad m{ m }^{ 2 }=\quad 120\quad m{ m }^{ 2 }
7 0
3 years ago
Read 2 more answers
A bag of candy weighs 25.62 ounces. A group of 4 friends is going to share the bag of candy equally.
saul85 [17]
Part A: 6.2
Part B:6.405
PArt C: The estimate was close to the real answer
4 0
3 years ago
Other questions:
  • A markdown that is less than 1%
    7·2 answers
  • Tina has 3/5 pound erase she will use 2/3 of it to make fried rice for her family how much rice with Tina used to make fried ric
    6·2 answers
  • The surface area of the triangular prism is?
    5·1 answer
  • Does anyone know this one i tried another website but it didn't help me
    10·1 answer
  • In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the d
    5·1 answer
  • Points W X and y are collinear (that is on the same line). Write and solve an equation to find m
    7·1 answer
  • Question 3 of 14
    15·1 answer
  • HELP ASAP PLZ HELP ASAP!!!!!
    13·2 answers
  • What is 8.05 × 10-5 in standard notation?
    6·2 answers
  • Can someone give the answer
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!