Answer:
Ribbon can't be enough
Step-by-step explanation:
Markin is making a flag shaped like a square. Each side measures 13 m. He wants to add ribbon along the edges. He has 48 m of ribbon. Does he have enough ribbon? If it is not enough,how much more ribbon needed?
Given :
Side length of square shaped flag = 13 m
Length of ribbon markin has to add along edges = 48 m
To know if the ribbon will enough ; we obtain the perimeter of the square shaped flag ;
4 * side length
4 * 13 = 52 meters
52 > 48
Since the perimeter is greater than the length of ribbon, then ribbon can't be enough
Answer:
p-value: 0.0367
Decision: Reject H₀
Step-by-step explanation:
Hello!
Hypothesis to test:
H₀:ρ₁-ρ₂=0
H₁:ρ₁-ρ₂>0
The statistic to use to test the difference between two population proportions is the approximation of Z
Z=<u> (^ρ₁-^ρ₂)-(ρ₁-ρ₂) </u> ≈N(0;1)
√ (<u>^ρ₁(1-^ρ₁))/n₁)+(^ρ₂(1-^ρ₂)/n₂))</u>
Z=<u> (0.28-0.15)-0 </u>= 1.79
√ (<u>0.28(1-0.28)/200)+(0.15(1-0.15)/300)</u>
p-value
Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
P(Z>1.79)= 0.0367
Conclusion:
Comparing the p-value against the significance level, you can decide to reject the null hypothesis.
I hope you have a SUPER day!
Answer:
There are at least two runners whose times are less than 9 seconds apart.
Step-by-step explanation:
Let's assume that Tₙ is the time of the n-th runner, we know that:
6 min < Tₙ < 7 min
knowing that:
1 min = 60 s
We can rewrite this as:
6*60 s < Tₙ < 7*60 s
360 s < Tₙ < 420 s
We know that there are 7 runners, and we want to see if we can conclude that there are two runners whose times are less than nine seconds.
So, the smallest time allowed in seconds is 361 seconds (the first value larger than 360 seg) while the largest time allowed is 419 seconds (the largest time allowed smallest than 420 seconds).
Now, let's assume that the first runner has the smallest time:
then:
T₁ = 361 s
Now let's add 9 seconds to the time of each runner (here we want to check that we can have all the runners with exactly 9 seconds apart in their times, so we will prove that the statement is false), then:
T₂ = 361s + 9s = 370s
T₃ = 370s + 9s = 379s
T₄ = 379s + 9s = 388s
T₄ = 388s + 9s = 397s
T₅ = 397s + 9s = 406s
T₆ = 406s + 9s = 415s
T₇ = 415s + 9s = 424s
But 424s > 420s
So this is not allowed (as the maximum time allowed was 419 s), so at least two of the runners must have times that are less than 9 seconds apart.
Then; Can you conclude that there are two runners whose times are less than nine seconds apart? Yes.
Answer: 5
Step-by-step explanation:
<h2>
Answer with explanation:</h2>
Let be the population mean.
Null hypothesis :
Alternative hypothesis :
Since the alternative hypothesis is left tailed, so the test is a left-tailed test.
Sample size : n=5 <30 , so we use t-test.
Test statistic:
Critical t-value for t=
Since, the absolute value of t (1.79) is less than the critical t-value , so we fail to reject the null hypothesis.
Hence, we have sufficient evidence to support the company's claim.