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
Anna35 [415]
3 years ago
14

Daily-high temperature measurements for 40 consecutive days are recorded for a particular city. The mean daily-high temperature

for this time period of 21.5 degrees Celsius is noted. Assuming that the sample standard deviation for all such temperatures is 1.5 degrees Celsius, test the claim that the population mean daily-high temperature is less than 22 degrees Celsius. Use P-value, significance level of 0.01, and determine conclusion.
(A) P-val = 0.979, fail to reject the null hypothesis
(B) P-val= 0.041, fail to reject the null hypothesis
(C) P-val=0.021, fail to reject the alternative hypothesis
(D) P-val=0.021, fail to reject the null hypothesis
(E) P-val = 0.041, reject the alternative hypothesis
Mathematics
1 answer:
Vesnalui [34]3 years ago
5 0

Answer:

t=\frac{21.5-22}{\frac{1.5}{\sqrt{40}}}=-2.108    

p_v =P(t_{39}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean temperature actually its NOT significant less then 22 at 1% of signficance.  

(D) P-val=0.021, fail to reject the null hypothesis

Step-by-step explanation:

1) Data given and notation  

\bar X=21.5 represent the mean for the temperatures

s=1.5 represent the sample standard deviation

n=40 sample size  

\mu_o =22 represent the value that we want to test

\alpha=0.01 represent the significance level for the hypothesis test.  

t 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 mean is less than 22C, the system of hypothesis would be:  

Null hypothesis:\mu \geq 22  

Alternative hypothesis:\mu < 22  

If we analyze the size for the sample is > 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

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

t=\frac{21.5-22}{\frac{1.5}{\sqrt{40}}}=-2.108    

P-value

We can calculate the degrees of freedom like this:

df=n-1=40-1=39

Since is a one left tailed test the p value would be:  

p_v =P(t_{39}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean temperature actually its NOT significant less then 22 at 1% of signficance.  

The best option would be:

(D) P-val=0.021, fail to reject the null hypothesis

You might be interested in
When Isabella left her house in the morning, her cell phone battery was partially charged. Let BB represent the charge remaining
SIZIF [17.4K]

Answer:

5% each hour

Step-by-step explanation:

in 1.5 hours she loses 7.5% of battery

get the percentage of loss for a half hour.

divide 1.5 and 7.5 by 3.

That gives a loss of 2.5% for every half hour.

Which gives a loss of 5% percent an hour.

6 0
2 years ago
What is the equation that models the sequence 6,12,24,48
labwork [276]
The equation that models the sequence is: 6+6 each time.
8 0
3 years ago
Read 2 more answers
Laws of Sines with find the angle.
Jobisdone [24]
A divide by sin A = b divide by sin B
1. 27 divide by sin 68=22 divide by sin x
Sin x=sin 68 times 22 divide by 27
Sinx=0.65696
X=71.7 degrees
4 0
3 years ago
Read 2 more answers
Use a geometric formula to solve the problem. A rectangle has a width of 4 centimeters and a perimeter of 26 centimeters. Find t
AURORKA [14]

The length is 9.

The formula to find the perimeter of a rectangle is

2L + 2W = P.

2L + 2(4) = 26.

2L + 8 = 26.

2L + 8 (-8) = 26 (-8).

2L = 18.

2L/2 = 18/2.

L = 9.

8 0
3 years ago
Bert and Eamie ran the 100-meter dash. The difference of their times was 1.5 seconds. If Bert win the race in a time of 12.6 sec
Bingel [31]

Answer:

Ernie's time is 11.1 seconds

Explanation:

If Bert won the race with the time of 12.6 and the time difference is 1.5, this means Ernie's time was 1.5 seconds less than 12.6.

12.6

−

1.5

=

11.1

5 0
3 years ago
Other questions:
  • Solve r = (9–9) for p.
    10·2 answers
  • Lily earned 317 pokemon go points. Sophia earned 25 times the amount of points lily earned. How many points did sophia earn?
    13·2 answers
  • 35.75÷3.64 please help help wanted
    10·1 answer
  • Please help me. I can’t figure out how to put this in the calculator
    9·1 answer
  • Select all of the factors of x3 + 5x2 + 2x – 8.
    8·2 answers
  • A watch was on sale for 70% off. The sale price is $60. What was the original price?
    9·1 answer
  • Help me plz don’t get it
    11·2 answers
  • PLEASE HELP Find the slope and equation of the tangent to each of the following curves at the given point:
    9·1 answer
  • What is the distance between points (-3 -5) and (-3 -7)?<br> Please help I’m tryna bring up my grade
    13·2 answers
  • The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!