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
kakasveta [241]
2 years ago
11

A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. ​a) E

stimate the percentage of all males who identify themselves as the primary grocery shopper. Use a 98​% confidence interval. Check the conditions first. ​b) A grocery store owner believed that only 43​% of men are the primary grocery shopper for their​ family, and targets his advertising accordingly. He wishes to conduct a hypothesis test to see if the fraction is in fact higher than 43​%. What does your confidence interval​ indicate? Explain. ​c) What is the level of significance of this​ test? Explain.
Mathematics
1 answer:
polet [3.4K]2 years ago
4 0

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) \alpha =1-0.98=0.02

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq  p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and z_{\alpha/2} is the z-value that let a probability of \alpha/2 on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, \alpha by 0.02 and z_{\alpha/2} by 2.33

Where p' and \alpha are calculated as:

p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02

So, replacing the values we get:

0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq  p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence 1-\alpha is equal to 98%

It means the the level of significance \alpha is:

\alpha =1-0.98=0.02

You might be interested in
HEY GUYS I NEED HELP LIKE REALLY BAD I HAVE A DBA( test) WHATS EVERYTHING I NEED TO KNOW ABOUT Exponential Functions PLZZZZ HELP
Angelina_Jolie [31]

Answer:

An exponential function can describe growth or decay

It gets rapidly smaller as x increases, as illustrated by its graph. In the exponential growth of f(x), the function doubles every time you add one to its input x.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
There are 48 skittles in a bag but 12 are red.What percentage are NOT red skittles
IgorLugansk [536]

75% of the skittles are not red.

This is figured out by dividing 12 by 48. So you get .25 (25%) of the skittles are red, yeah? After that, you just subtract 25 from 100, and boom! 75% of the skittles are not red.

5 0
2 years ago
Alicia´s gross monthly pay is 1,700. Alicia pays 1.25% of her monthly salary for Medicare. how much dose she pay
loris [4]

Answer:

$21.25

Step-by-step explanation:

1700 x 1.25% = 1700 x 0.0125 = 21.25

So Alicia's paying $21.25 of her monthly salary to Medicare.

4 0
3 years ago
Read 2 more answers
Indicate the answer choice that best completes the statement or answers the question.
ch4aika [34]

Answer:

no.D) 18% is the answer of this question

8 0
3 years ago
Please help!!!! I need this ASAP Help
Nutka1998 [239]

Answer:

Step-by-step explanation:

If x is -1, then the point on the parabol is (-1,4)

If x is 0, then the point on the parabol is (0,-2)

If x is 1, then the point on the parabol is (1,-6)

8 0
3 years ago
Other questions:
  • 381.10-214.43 equals
    9·1 answer
  • I need help with a problem
    5·1 answer
  • (-3/14)+5/7hhggygwfghx
    9·1 answer
  • Enter the equation described in this sentence.<br>The product of 12 and j is equal to 75.6.<br>​
    5·2 answers
  • which equation has only one solution? A. 6r = 5r + r B. 4m + 5 =25 C. 8v + 11=8v +11 D. 2 - 3p = -3p +5
    10·1 answer
  • 5*(*=2) + 7? Please show work although it's not necessary:D
    8·1 answer
  • Find the midpoint between points F(-5, -18) and K(15,8).
    8·2 answers
  • Graph each equation.<br> (i really just need to know the points... ty!)
    12·2 answers
  • Which of the following is a solution to <br><br>​
    7·1 answer
  • PLEASE HELP ME, I'm falling in math class!! PLEASE ​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!