Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 1
4, 25, 17, 28, 15, 21. Use Table 2.a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places, "sample mean" to 3 decimal places and "sample standard deviation" to 2 decimal places.) Sample mean Sample standard deviation b. Construct the 80% confidence interval for the population mean. (Round "t" value to 3 decimal places, and final answers to 2 decimal places.) Confidence interval to c. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places, and final answers to 2 decimal places.) Confidence interval to d. What happens to the margin of error as the confidence level increases from 80% to 90%?As the confidence level increases, the interval becomes narrower.As the confidence level increases, the interval becomes wider.
1 answer:
Answer:
a: Sample mean: 20, Sample standard deviation: 1.732
b: 19.13 <µ < 20.87
c: 18.84< µ < 21.16
d: as the confidence level increases, the interval becomes wider
Step-by-step explanation:
a: Sample mean is found by adding up all the individual values of the sample, then dividing by the total number of values in the sample.
Sample standard deviation is the square root of the variance
See the first attached photo for the calculations of these values.
We need to create a 80% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.
Look for the column on the t-distribution chart that has "area in two tails" of 0.20 (80%), and row 7 (degree of freedom)
The t-value is 1.415
See the second attached photo for the construction of the confidence interval
We need to create a 90% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.
Look for the column on the t-distribution chart that has "area in two tails" of 0.10 (90%), and row 7 (degree of freedom)
The t-value is 1.895
See the third attached photo for the construction of the confidence interval
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Answer:
0.46 (46%)
Step-by-step explanation:
We have the following data:
- Probability that player V wins the first set:
(because the text says the two players are equally likely to win the first set)
- Probability that player V wins the 2nd set if he has won the 1st set:
So, the probability that player V wins the first 2 sets is:
(1)
Instead, the probability that player V loses the 2nd set if he has won the 1st set is 0.40 (=1-0.60), so
So, the probabiity that player V winse the 1st set but loses the 2nd set is
(2)
Also, we have:
- Probability that player V loses the 1st set:
- Probability that she will lose the 2nd set in this case is 0.70, it means that the probability that she will win the 2nd set if she lost the 1st set is 0.30, so:
So, the probability that she will lose the 1st set and win the 2nd set is:
(3)
Combined together (2) and (3), this means that the probability that player V wins exactly 1 set out of the first two sets is:
(4)
At this point, the probability that she will win the 3rd set is
This means that the overall probability that she will win the 3rd set if she won exacty 1 of the first 2 sets is:
(5)
So, the overall probability that player V will win a match against player M is the sum of (1) and (5):
Answer:
The answer is below
Step-by-step explanation:
From the image of the leaning tower of Pisa, we can see that it passes through the point (7.75, 0) and (10.75, 42).
a) The equation of a line in slope intercept form is given by y = mx + b, where m is the slope and b is the intercept. Also, the equation of line passing through
Hence since it passes through (7.75, 0) and (10.75, 42), the equation is:
b) When the tower is 56 meters tall, i.e. y = 56, we need to find the value of x:
y = 14x - 108.5
56 = 14x - 108.5
56 + 108.5 = 14x
164.5=14x
x = 164.5/14
x = 11.75
When the tower is 56 meters tall, the top of the tower is 11.75 m off center
Answer:
En 5 horas se habrá enterado todo el pueblo.
Step-by-step explanation:
Sabemos que en un pueblo 5 personas escucharon una noticia.
Una hora más tarde, cada una de ellas le contó la noticia a otras 5.
Luego, éstas contaron la noticia a otras 5 y así sucesivamente.
Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.
La ecuación a desarrollar para resolver el problema es la siguiente :
Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.
Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :
(I)
Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :
(II)
Buscamos el valor de que satisface la ecuación (II).
Probando y realizando las sumas encontramos que :
El valor de que satisface (II) es
.
Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.
Entonces para nuestro , el número de horas que pasaron son 5 horas (1 menos que el valor de
)
Todo el pueblo se habrá enterado en 5 horas de la noticia.