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
tiny-mole [99]
3 years ago
11

A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is s

ignificantly different from the national average. A random sample of 50 five-person families in San Antonio showed a mean of $133.474 and a standard deviation of $11.193. Assume that the national average weekly grocery bill for a five-person family is $131.
Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?
Mathematics
1 answer:
bogdanovich [222]3 years ago
8 0

Answer:

No, the sample evidence is not statistically significant (P-value = 0.125).

To reject the null hypothesis, the P-value has to be smaller than the significance level, so the significance level to reject the null hypothesis has to be 0.125 or higher.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average weekly grocery bill per five-person family in San Antonio is significantly different from the national average.

Then, the null and alternative hypothesis are:

H_0: \mu=131\\\\H_a:\mu\neq 131

The significance level is 0.05.

The sample has a size n=50.

The sample mean is M=133.474.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.193.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{11.193}{\sqrt{50}}=1.583

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{133.474-131}{1.583}=\dfrac{2.474}{1.583}=1.563

The degrees of freedom for this sample size are:

df=n-1=50-1=49

This test is a two-tailed test, with 49 degrees of freedom and t=1.563, so the P-value for this test is calculated as (using a t-table):

P-value=2\cdot P(t>1.563)=0.125

As the P-value (0.125) is bigger than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the average weekly grocery bill per five-person family in San Antonio is significantly different from the national average.

You might be interested in
Have to find volume and surface area but idk how
Setler [38]

Answer:

volume 1050 in^{3}

surface area 859 in^{2}

Step-by-step explanation:

volume is length times width times height (7*25*12)/2

surface area is area of all the sides added together

2(25*12)+(12*7)+ 2(\frac{7*25}{2})

4 0
3 years ago
Read 2 more answers
Please help! :) Need answer fast!
Vlada [557]

Answer:

x = 3

y = 2

Step-by-step explanation:

When 2 triangles are congruent, they will have exact same 3 sides length and exact same 3 angles measure.

So we can say:

-2x + 6y = 6

and

-7x + 8y = -5

Let's multiply first equation by 7 and 2nd equation by -2, to get:

7 [-2x + 6y = 6] = -14x +42y = 42

and

-2 [-7x + 8y = -5] = 14x - 16y = 10

Now adding these 2 new equations and solving for y:

-14x +42y = 42

14x - 16y = 10

----------------------

26y = 52

y = 52/26

y = 2

Now we put y = 2 into 1st equation (or any other) and solve for x:

-2x + 6y = 6

-2x + 6(2) = 6

-2x + 12 = 6

6 = 2x

x = 6/2

x = 3

5 0
3 years ago
Which values from the set{5,7,9,11,13} make the inequality w-4<8 true?
Rasek [7]

Answer:

5, 7, 9, 11

Step-by-step explanation:

Solve the inequality

w - 4 < 8 ( add 4 to both sides )

w < 12

w ∈ { 5, 7, 9, 11 }

7 0
3 years ago
A and b are positive integers and a–b = 3. Evaluate the following: 27^ (1/3 b)/9^ (1/2 a)
maxonik [38]

Answer:

1/27

Step-by-step explanation:

27^(b/3)/9^(a/2) = (27^(1/3))^b/(9^(1/2))^a = (3^b)/(3^a) = 3^(b-a)

= 3^(-(a-b)) = 3^-3 = 1/3^3 = 1/27

5 0
3 years ago
Which of the following can cause market failure?
nalin [4]

Answer: C

Step-by-step explanation: not enough information

5 0
3 years ago
Other questions:
  • 7+x/3 = 2x-5 Please help with my maths question
    14·2 answers
  • A bicycle shop advertised all mountain bikes were priced at 1/4 discount.
    14·1 answer
  • What is the square root of 975
    6·2 answers
  • a person invests $2560 in an account that earns 5.2% annual interest. find when the value of the investment reaches $6000
    5·1 answer
  • Jamie mixed 2/3 bottle of cranberry juice and 5/6 bottle of orange juice.Which shows how to compare 2/3 and 5/6?
    6·1 answer
  • My friend and I have different calling plans. Mine has a monthly fee of $10 and $0.08 per minute charge. My friend pays $0.06 a
    12·1 answer
  • Which of the following circles have their centers in the x-axis check all that apply
    9·1 answer
  • The graph shows the relationship between time and the number of sodas bottles a machine can make. Use the points (5,100) and (7,
    14·1 answer
  • Slope <br>y intercept <br>x intercept​
    13·1 answer
  • In the diagram below, BC−→− bisects ∠FBE
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!