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
Ivenika [448]
3 years ago
11

A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is current

ly producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done at the 10% level of significance to help make the decision.
Mathematics
1 answer:
vladimir2022 [97]3 years ago
6 0

Answer:

z=\frac{7.1-7.4}{\frac{1.2}{\sqrt{36}}}=-1.5  

Since is a left sided test the p value would be:  

p_v =P(z  

Comparing the p value and the significance level given \alpha=0.1 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly lower than 7.4 minutes at 10% of significance

Step-by-step explanation:

Data given and notation  

\bar X=7.1 represent the sample mean    

\sigma=1.2 represent the population standard deviation

n=36 sample size  

\mu_o =7.4 represent the value that we want to test  

\alpha=0.1 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean i lower than 7.4, the system of hypothesis would be:  

Null hypothesis:\mu \geq 7.4  

Alternative hypothesis:\mu < 7.4  

The statistic is given by

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{7.1-7.4}{\frac{1.2}{\sqrt{36}}}=-1.5  

P-value  

Since is a left sided test the p value would be:  

p_v =P(z  

Conclusion  

Comparing the p value and the significance level given \alpha=0.1 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly lower than 7.4 minutes at 10% of significance

You might be interested in
42,300 multiply by 10 can someone show the work
Assoli18 [71]
       10
x42,300
-------------
          00
        000
     3,000
   20,000
400,000
-------------
423,000
3 0
3 years ago
Read 2 more answers
Which equation represents the graph? (y-1)^2/49-x^2/81=1 (y-1)^2/7-x^2/9=1
Anon25 [30]

Answer: A, (y-1)^2/49-x^2/81=1

7 0
3 years ago
Simplify to create a equivalent expression.
Ratling [72]

Answer:

\boxed{\bold{66k+9}}

Explanation:

Expand \bold{5\left(10k+1\right): \ 50k+5}

= \bold{50k+5+2\left(2+8k\right)}

Expand \bold{2\left(2+8k\right): \ 4+16k}

= \bold{50k+5+4+16k}

Simplify \bold{50k+5+4+16k: \ 66k+9}

= \bold{66k+9}

Mordancy.

7 0
3 years ago
Read 2 more answers
Given that you have 2 parallel lines cut by a transversal, what is the measure of angle 2?
Archy [21]

Step-by-step explanation:

angle 2 = 2x + 10 deg (corresponding angles) or 180 - 4x + 46 deg (angles on a straight line are supplementary)

therefore,

2x + 10 = 226 - 4x

6x = 216

x = 36

hence,

angle 2 = 2(36) + 10 = 82deg

Topic: Angles

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

4 0
3 years ago
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not
Lorico [155]

Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

  • C_x^n=n!/(n-x)!x!   (i.e. combination)
  • x= total number of successes
  • p=probability of success (p=1-q)  
  • q=probability of failure (q=1-p)
  • n=number of trials
  • P(X)= probability of total number of successes

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

3 0
3 years ago
Other questions:
  • A car factory can build 14 cars in 4 hours. <br><br> How many cars can it build in 7 hours?
    13·1 answer
  • Please answer this<br> X+2y=6<br> 3x-y= -10
    6·1 answer
  • 2) Find the GCF of 35 and 28​
    12·2 answers
  • On a coordinate plane, the x-axis is labeled Turkey hot dogs and the y-axis is labeled dollars. Points (2, 1) and (4, 2) are plo
    12·2 answers
  • HELP AGANI PLZ
    13·1 answer
  • What is the length of side s of the square shown below? 8 90"
    5·2 answers
  • How many solutions does 17.75x + 24 = 18.95x + 18 have?
    15·1 answer
  • PLEASE HELP!!*URGENT**
    15·1 answer
  • Aliana uses beads that are 5/4 Centimeters long she uses three beads altogether how many centimeters of beads will Aliana use fo
    13·1 answer
  • Maureen says that if a system of linear equations has three equations, then there could be exactly two solutions to the system.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!