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Neko
18 days ago
8

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of

type A​ (the original​ paint) and 9 cans of type B​ (the modified​ paint) were selected and applied to similar surfaces. The drying​ times, in​ hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following​ 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2​, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population​ means? 4.90 hrless than
Mathematics
1 answer:
AnnZ [9K]18 days ago
7 0

This question lacks complete information. I retrieved the full segment (the part in bold) from Google:

The derived 98% confidence interval for μ1 - μ2, indicating the difference between the average drying durations for paint cans of type A and type B:

4.90 hours < μ1 - μ2 < 17.50 hours.

Answer:

A paint producer enhanced the formulation to reduce drying time. Independent random samples of 11 cans of type A​ (original paint) and 9 cans of type B​ (modified paint) were collected and applied to similar surfaces. Drying times, measured in hours, were documented. The summarized statistics include: Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The subsequent 98% confidence interval for μ1 - μ2 indicates that the mean drying time for paint cans of type A exceeds that for type B. What implication does the confidence interval have on the population means?

The mean difference suggested by the 98% confidence interval indicates that drying times for the two paint types are between 4.90 and 17.50 hours. This suggests that Type A paint requires between 4.90 and 17.50 hours longer to dry compared to Type B paint.

Step-by-step explanation:

The mean difference for the 98% confidence interval indicates that drying times for the two paint types lie between (4.90, 17.50). This suggests that Type A paint takes from 4.90 to 17.50 hours more to dry than Type B paint.

The confidence interval consists entirely of positive values, indicating that the average drying time for paint type A exceeds that of paint type B. The adjustment seems effective in minimizing drying times.

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Frank reasoned that in the number 0.555, the value of the 5 in the thousands place is ten times as great as the 5 in the hundred
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The provided number is 0.555, which can also be expressed as

0+ \frac{1}{10}*5 + \frac{1}{100}* 5+ \frac{1}{1000} * 5

In examining the digits post-decimal, each subsequent digit decreases to 1/10 of the preceding one.

Thus, the assertion that "the value of the 5 in the thousands place is ten times as great as the 5 in the hundredth place" is incorrect.


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12 days ago
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Three irrational numbers are given below. Select the option that correctly plots the approximate value of each me on live where
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The value you are seeking is 2
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28 days ago
Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de
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Respuesta:

La altitud del globo por encima del nivel del suelo es de 449,6 metros.

Explicación paso a paso:

El enunciado no está completo. El texto completo es: "Un globo se desplaza entre las ciudades A y B, que se encuentran a 1.500 m de distancia. Los ocupantes del globo observan la ciudad A con un ángulo de depresión de 27°, mientras que, para la ciudad B, el ángulo es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?"

El diagrama que ilustra esta situación está en el archivo adjunto. Para calcular la altura del globo, se pueden emplear las funciones trigonométricas, siendo recomendable hacer uso de la función tangente para los ángulos de depresión mencionados:

Ciudad A

\tan 27^{\circ} = \frac{h}{1500\,m-x}

0,510 = \frac{h}{1500\,m-x}

Ciudad B

\tan 36^{\circ} = \frac{h}{x}

0,727 = \frac{h}{x}

Donde h y x representan la altura desde el suelo y la distancia horizontal desde la ciudad A.

Luego, se igualan las alturas en ambas ecuaciones para calcular la distancia horizontal del globo en relación a la ciudad A:

0,727\cdot x = 0,510\cdot (1500\,m-x)

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x = 618,432\,m

Por último, la altura del globo sobre el suelo se calcula como:

h = 0,727\cdot x

h = 0,727\cdot (618,432\,m)

h = 449,600\,m

La altura del globo respecto al nivel del suelo es 449,6 metros.

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1 month ago
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P(A and B)= 0.14 + 0.31 - 0.14=0.31

Therefore, the required probability is: 0.31

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