A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a 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 size of 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision

Required:
a. For a test with a level of significance of 0.10, compute the critical value; set up the appropriate hypotheses and the calculate the p-value of the test
b. Will the null hypothesis will be rejected with a level of significance of 0.10? Explain why or why not?

Answers

Answer 1

Using the z-distribution, we have that:

a)

The hypothesis test is:

[tex]H_0: \mu = 7.4[/tex][tex]H_1: \mu < 7.4[/tex]

The p-value is of 0.0668.

The critical value is [tex]z^{\ast} = -1.28[/tex]

b) Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.

Item a:

At the null hypothesis, it is tested if the mean is of 7.4 minutes, that is:

[tex]H_0: \mu = 7.4[/tex]

At the alternative hypothesis, it is tested if the mean is lower than 7.4 minutes, that is:

[tex]H_1: \mu < 7.4[/tex]

We have the standard deviation for the population, hence, the z-distribution is used.

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.

For this problem, the values of the parameters are: [tex]\overline{x} = 7.1, \mu = 7.4, \sigma = 1.2, n = 36[/tex].

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{7.1 - 7.4}{\frac{1.2}{\sqrt{36}}}[/tex]

[tex]z = -1.5[/tex]

Using a z-distribution calculator, the p-value is of 0.0668.

Also using a calculator, considering a left-tailed test, as we are testing if the mean is less than a value, the critical value with a significance level of 0.1 is of [tex]z^{\ast} = -1.28[/tex].

Item b:

Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.

You can learn more about the use of the z-distribution to test an hypothesis at https://brainly.com/question/16313918


Related Questions

Question 1 (1 point)
When a transversal passes through two lines and the corresponding angles are
congruent, then the lines are parallel.
True
False

Answers

Answer:

True

Step-by-step explanation:

If corresponding angles are congruent, the lines are parallel

1 thor 10 HOW DOSE MY DOG LOOK

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I would say a solid 9

So cute!!!!!!!!!!!!!!!!!!

A regular hexagon is rotated 360° about its center. How many times does the image of the hexagon coincide with the pre image during the rotation?
A. 1 time
B. 3 times
C. 12 times
D. 6 times

Answers

The image of the regular hexagon coincides with the pre-image 6 times during rotation.

A regular hexagon is a polygon that has six equal sides and six equal angles.

In a single rotation which is usually the rotation of an object at 360°, the number of times in which the regular hexagon coincides with its pre-image is 6 times, this is because it has 6 equal sides and 6 equal angles.

Learn more about regular polygon here:

https://brainly.com/question/1592456

Answer:

6

Step-by-step explanation:

I just took the test

Find the area of the shaded rectangle by multiplying its length and width. Fill in the equation.

Answers

Answer:

5

Step-by-step explanation:

6/7 x 5/7 = 35/7

35/7 = 5

solve similar triangles (advanced)

Answers

Answer:

1

Step-by-step explanation:

They are similar triangles and ED and AD are 9 so CB and AB must be 1.

How many inflection point(s) do you see ?

Answers

Answer:

  7

Step-by-step explanation:

There is a point of inflection at each point where the graph crosses the line y=2. There are 7 points of inflection shown.

__

A point of inflection is where the graph changes from being concave downward to concave upward, or vice versa. For a sine function, that is everywhere the function crosses its midline.

Answer:

7 inflection points

Step-by-step explanation:

The given function [tex]f(x)=sinx+2[/tex] has a midline of y=2 where each point of the function that intersects the line is an inflection point. Inflection points are where the concavity changes, defined by when the second derivative is equal to 0 or undefined.

[tex]f(x)=sin(x)+2[/tex]

[tex]f'(x)=cos(x)[/tex]

[tex]f''(x)=-sin(x)[/tex]

[tex]0=-sin(x)[/tex]

[tex]x=\pi n[/tex] for any integer [tex]n[/tex]

From [tex][-10,10][/tex], there are 7 inflection points, which are[tex]x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi[/tex]

If AB is parallel to CD and the slope of AB is -3, what is the slope of CD

Answers

Answer:

-3

Step-by-step explanation:

The slopes of parallel lines are equal.

If two lines are parallel (that means they are at the same angle, they are always the same distance apart and they never cross), then they have the same slope. Both lines have slope -3

Answer:

-3

Step-by-step explanation:

There is a rule in math that if two slopes are parallel, they must have the same slope. Let's answer the question with this first.

So AB is parallel to CD, meaning they must have the same slope. If AB's slope is -3, then so must CD's. That's the answer to the question.

Coming back to the parallel slope rule, why does this work? Well, if two lines are parallel, it means they never will touch each other, meaning they rise, fall, bend, curve, etc... at the same rate. The slope is the change in how much the line rises divided by the change in how much it runs (moves horizontally). That proves the rule.

Please consider a brainliest, thank you!

0. CHARITY Cain collects money on the weekends for his favorite charity. The
past four weekends he collected $105, $170, $132, and $165. How much
does he have to collect on the fifth weekend to average at least $150 for
the five weekends?

Answers

Answer:

He needs to get $178 to average at least $150.

Step-by-step explanation:

105, 132, 165, 170, and 178 has an average of 150.

which is equivalent to 2^-3/2^2

Answers

Answer:

[tex]1/32[/tex]

Step-by-step explanation:

To understand this question you would first of all need to know about negative exponents and multiply fraction by integers.

Example I would like to find out [tex]2^{-2}[/tex],

You would first normally solve this question by squaring, which would result in 4 then divide it by 1. Like this: [tex]1/2^{2}[/tex]

Which would be 0.25 or 1/4

Lets apply this knowledge to the following question:

1. [tex]2^{-3} / 2^{2}[/tex]

2. [tex]\frac{1}{8} / 4[/tex]

3. [tex]1/32[/tex]

f(x)=-x^2-7x+9 find 7f(x)

Answers

Answer:

do it got a picture

on the edge

Step-by-step explanation:

1/2 of a bowl of cereal is divided equally between 4 bowls. how much cereal is in each bowl

Answers

Answer:

1/16 of the cereal is in each bowl

Step-by-step explanation:

Answer:

1/8  

Step-by-step explanation:

1/2 / 4

= 1/2 * 1/4

= 1/8.

thirty tickets were sold for a concert, some at 60 cent and the rest is at $1. If the total was raised to $22, how many had the cheaper tickets.

Answers

Answer:

20

Step-by-step explanation:

To solve this question we can use a system of linear equations. The 2 equations should represent- 1) the number of total tickets sold and 2) the total amount raised. So, the two equations look like this (in this situation, let x stand for the cheaper tickets and y for the more expensive ones).

x+y=300.6x+1y=22

Then, there are multiple ways to solve this including graphing, elimination, and substitution. In my opinion, substitution is the best for this situation.

Firstly, isolate the y variable in the first equation

y=30-x

Next, plug in this value for y in the second equation

0.6x+(30-x)=22

Then, solve this equation algebraically

x=20

Since x stands for the cheaper tickets, we know that 20 people bought the cheaper tickets.

Find the 75th term of the arithmetic sequence
16, 15, 14,

Answers

Answer:

[tex]a_{75}=-58[/tex]

Step-by-step explanation:

This is an arithmetic sequence:

[tex]a_n=a_1+(n-1)d[/tex]

where d is the common difference and n is the index of any given term.

For the given sequence, the common difference is -1:

[tex]15-16=-1\\14-15=-1[/tex]

Knowing both the common difference and the first term, you can write the equation for this sequence:

[tex]a_n=16+(n-1)(-1)[/tex]

Then you can use that equation to find the 75th term:

[tex]a_{75}=16+(75-1)(-1)\\a_{75}=16+(74)(-1)\\a_{75}=16-74\\a_{75}=-58[/tex]

x+2=-14x
do anyone know this need it for hw

Answers

Answer:

if you was asking for *solve for X* it is -2/15

Step-by-step explanation:

sorry if this dose not help

Can someone plz help Me? :(

Answers

the greatest common factor of 48 and 60 is D.) 12

Answer:

Answer: D or 12

Step-by-step explanation:

This one is fairly simple.

The Greatest Common Factor is the largest number that can go into both 48 and 60...

What I did is simply took the largest number from the answer choices: which is 12 and then divided 48 and 60 by 12 each. 12 can go into both of these number whole so 12 is your greatest common factor.

Find the perimeter of the figure shown to the right.

Answers

Step-by-step explanation:

that is very simple. you do understand the word "perimeter" ? it just means the distance when walking around the whole shape once.

and that clearly means to just add all side lengths.

that's it.

so, 25 + 18 + 18 + 20 + 17 = 98 ft

was there any other problem with this you did not understand ?

45 + 30 = 100 - w
Answer correctly luvs

Answers

Answer:

the answer is 25

Step-by-step explanation:

45+30=100-w

then your going to subtract 45 on both sides. So 100-45 is 55.

so now your equation looks like this

30 = 55 - w

subtract 55 on both sides so you will have -25 = -w. Then your going to divide -w on both sides and you will have positive 25

i hope thus helps

Peter has 100$. The price of a watch is 60$. If Peter gets 25% discount,can he buy 2 watches?

Answers

yes.

25 percent discount means that the price of one watch is 45 dollars.

45 plus 45 is less than 100.

Answer:

The answer is yes.

Step-by-step explanation:

25% = divide by 4

25% of 60$ = 60$ divided by 4 = 25$

So then we need to do 60$ - 25$ which equals to 45$.

45$ + 45$ = $90.

Hope that helps. x

X=-2y,x-y=9 solve by substitution SHOW ALL WORK

Answers

Answer:

x = 6, y = -3

Step-by-step explanation:

x = -2y

x-y = 9

Substitute x = -2y into the equation.

;(-2y)-y = 9

-3y = 9

y = 9/-3

y = -3

Substitute y = -3 into the equation.

x = -2y

x = -2(-3)

x = 6

Helpp with number 23 pls

Answers

Answer : Susan is correct

Susan is correct because if you get that chart and turn all the numbers to decimals and divide the chart in half you will get the answer to 1.4/0.2 because the chart has 14 slots and if you divide that by 2 you will get 7 just think of 1.4/0.2 as 14/2.

I want help its urgent!!!

(iv), (v), (vi) Questions​

Answers

Solution:

iv) Given equation: [tex]x^{2} - y^{2} - 4x - 2y + 3[/tex]

Since we are given two variables, we need to split the original expression into two quadratic expressions as

[tex]x^{2} - 4x + 4 - y^{2} - 2y - 1[/tex]

Factoring x first:

[tex]x^{2} - 4x + 4 =[/tex] [tex]x^{2} - 2x - 2x + 4[/tex]

= [tex]x (x - 2) - 2 (x-2)[/tex]

= [tex](x-2)(x-2)[/tex]

[tex]= (x-2)^{2}[/tex]

Factoring y now:

[tex]-y^{2} - 2y - 1 = -1(y^{2} + 2y + 1)[/tex]

= [tex]-1(y^{2} + y + y + 1)[/tex]

= [tex]-1[ y(y+1) + 1(y+1)][/tex]

= [tex]-1 [(y+1)(y+1)][/tex]

= [tex](y+1)(-y-1)[/tex]

Therefore, the original expression becomes

[tex](x-2)^{2}+(y+1)(-y-1)\\or \\(x-2)(x-2) + (y+1)(-y-1)[/tex]

At the movies, tickets cost $12 for adults and $7 for kids under 12. How many total

tickets would someone get if they purchased 2 adult tickets and 16 kids tickets? How

many total tickets would someone get if they purchased a adult tickets and k kids

tickets?

Total tickets, 2 adult tickets and 16 kids tickets:

Total tickets, a adult tickets and k kids tickets:

Answers

Answer:

18a+k

Step-by-step explanation:

The total number of tickets is the sum of the number of adult tickets and the number of kid tickets.

  Total tickets, 2 adult tickets and 16 kids tickets: 2 +16 = 18

  Total tickets, a adult tickets and k kids tickets: a +k

_____

Additional comment

The total price is a different matter:

  $12(2) +$7(16) = $136 . . . for 2 adult and 16 kids

  12a +7k . . . for 'a' adults and 'k' kids

What is the answer please give i really help and no links

Answers

Answer:

[tex]9\frac{57}{63}[/tex]

Step-by-step explanation:

First, we need to turn them into improper fractions:

[tex]2\frac{4}{7}[/tex] + [tex]7\frac{3}{9}[/tex]

7 x 2 + 4

7 x 9 + 3

[tex]\frac{18}{7}[/tex] + [tex]\frac{66}{9}[/tex]

Next, we need to find a common multiple of both 7 and 9

7, 14, 21, 28, 35, 42, 49, 56, 63

9, 18, 27, 36, 45, 54, 63

So the denomonator turns into 63.

We've multiplied the denomonater 9 times for the first fraction and 7 times for the second fraction, we therefore have to do the same to the numerator.

18 x 9 = 162

66 x 7 = 462

[tex]\frac{162}{63}[/tex] + [tex]\frac{462}{63}[/tex] = [tex]\frac{624}{63}[/tex]

Next, we have to turn it back into a mixed number.

To work it out: 624 / 63 = 9 (1 s.f) <--- Mixed number.

9 x 63 = 567

624 - 567 = 57 (Working out the remainder.)

Combining them, the answer is therefore [tex]9\frac{57}{63}[/tex]

Hope this helps and have a good day!

What is 6 percent of 200 plz show your work

Answers

Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

200 * 0.06 = 12

a

Two taxi companies have different pricing systems. Company A charges a flat fee of $8 plus $0.10

per mile driven. Company B does not charge a flat fee, but charges $0.60 per mile driven. At what

distance do both companies charge the same amount?

Answers

Answer:

16 miles

Step-by-step explanation:

let the number of miles driven be = x

Company A = Company B

8 + 0.10x = 0.60x

8 = 0.50x

x = 16

Hi ~ just a quick note:

I just started uploading videos to yt that contains steps to solving a problem. I sometimes share an unlisted video link so you can view it.

https://youtu.be/XhqLj_YOLBM

-Chetan K

Today 60 students rode their bicycles to Coast Middle School. If this is 75% of the students at the school, how many students attend Coast middle School?

Answers

Answer:

i think students attend Coast middle School 80 students

Step-by-step explanation:

students attend Coast middle School x students

75%x = 60

x = 60×100/75

x = 80

Answer:

80 students attend

Step-by-step explanation:

75% is the same as 3/4 so you divide 60 by 3 to get 20 then you can multiply that by 4 to get 80

What is the value of x in the polygon below?

Answers

Answer:

x=141

Step-by-step explanation:

The measure of all the angles in a septagon (7 sided shape) add up to 900°. The current sum of the known angles 131°+122°+125°+148°+107°+126°=759°.

900° total sum minus known sum 759° equals 141°.

I honestly don’t know

Answers

Answer:

x=-3h

x=-12

Step-by-step explanation:

[tex]\frac{x}{h} +1=-2[/tex]

[tex]\frac{x}{h} =-3[/tex]

[tex]x=-3h[/tex]

[tex]x=-3(4)[/tex]

[tex]x=-12[/tex]

Simplify.

46‾√+26‾√−6‾√




56‾√

518‾‾‾√

618‾‾‾√

66‾√

Answers

618 hope this helps you have an amazing week

A candy company used 8 pints of chocolate to
make 2 boxes of candy. How much chocolate would
they need to make 6 boxes of candy?

Answers

Answer:

They would need 24 pints of chocolate to make 6 boxes of candy

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