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
Aneli [31]
3 years ago
7

A survey of 25 young professionals fond that they spend an average of $28 when dining out, with a standard deviation of $10. (a)

Find and interpret the 95% confidence interval for the average spending. (b) Based on your answer in part (a), can you conclude statistically that the population mean is less than $30? Explain

Mathematics
1 answer:
skad [1K]3 years ago
8 0

Answer:

a) The 95% of confidence intervals for the average spending

(23.872 , 32.128)

b) The calculated value t= 1< 1.711( single tailed test) at 0.05 level of significance with 24 degrees of freedom.

The null hypothesis is accepted

A survey of 25 young professionals statistically that the population mean is less than $30

<u>Step-by-step explanation</u>:

Step:-(i)

Given data a survey of 25 young professionals fond that they spend an average of $28 when dining out, with a standard deviation of $10

The sample size 'n' = 25

The mean of the sample   x⁻  = $28

The standard deviation of the sample (S) = $10.

Level of significance ∝=0.05

The degrees of freedom γ =n-1 =25-1=24

tabulated value t₀.₀₅ = 2.064

<u>Step 2:-</u>

The 95% of confidence intervals for the average spending

((x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha }\frac{S}{\sqrt{n} } )

(28 - 2.064 \frac{10}{\sqrt{25} } ,28 + 2.064\frac{10}{\sqrt{25} } )

( 28 - 4.128 , 28 + 4.128)

(23.872 , 32.128)

a) The 95% of confidence intervals for the average spending

(23.872 , 32.128)

b)

Null hypothesis: H₀:μ<30

Alternative Hypothesis: H₁: μ>30

level of significance ∝ = 0.05

The test statistic

t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }

t = \frac{28-30 }{\frac{10}{\sqrt{25} } }

t = |-1|

The calculated value t= 1< 1.711( single tailed test) at 0.05 level of significance with 24 degrees of freedom.

The null hypothesis is accepted

<u>Conclusion</u>:-

The null hypothesis is accepted

A survey of 25 young professionals statistically that the population mean is less than $30

You might be interested in
A bag contains 10 pounds of dog food. A family feeds their dogs 0.85 pound of dog food a day. How much dog food is left in the b
tensa zangetsu [6.8K]
A bag contains 10 pounds of dog food.

A family feeds their dogs 0.85 pound of dog food a day so cin seven day the dog eats (0.85 x 7) = 5.95 pounds

so, <span>dog food is left in the bag after 7 days is </span>(10-5.95) = 4.05 pounds


8 0
3 years ago
Read 2 more answers
Help me with this problem like the whole thing
Ulleksa [173]
Has to multiply I think try that !
3 0
3 years ago
What is the value of this expression 14−3? 164 112 12 64
Firlakuza [10]

Answer:

11

Step-by-step explanation:

14-3 = 11

you have 14 apples and you eat 3 of them. wow! now you have 11 apples!

4 0
3 years ago
ada recorded the thickness a of a set of books. This line plot shows her results. Jada stacked the books that were 112 inches th
Sergeu [11.5K]
Good game play later
5 0
2 years ago
Factor completely
ZanzabumX [31]
Use the (-b + - sqrt( b^2 - 4ac) ) /2a Formula.
a = 1 b= 10 c= 24
 so you get .. (x+6 )(x+4) A
 
4 0
3 years ago
Other questions:
  • A steel mill has fixed costs of $100 per hour and variable costs of $50 per hour. what will happen to these costs if the mill cl
    6·2 answers
  • Why is it important to consider using tools when you are solving a problem.
    5·1 answer
  • Write a word phrase for the algebraic expression: 2t-9
    14·2 answers
  • The volume of a cube is 343 cubic yards what is the length of the cube
    14·1 answer
  • What are the zeros of the quadratic function f(x) = 6x^2 + 12x – 7?
    9·1 answer
  • What is the range of the relation {(2, 4), (3, 4), (4,7), (5,7), (6,5)}?
    9·1 answer
  • If an object is propelled upward from a height of 48 feet at an initial velocity of 96 feet per second, then its height after t
    8·1 answer
  • YOUR TURN<br><br> Please help I am really confused
    14·1 answer
  • The result of a game is Win, Lose or Draw.
    9·1 answer
  • In a scientific study there are 7 guinea pigs, 4 of which are pregnant. If 3 are selected at random without replacement, find th
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!