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Chapter 10: Q. R10.4 (page 696)

Candles A company produces candles. Machine 1 makes candles with a mean

length of 15cm and a standard deviation of 0.15cm. Machine 2 makes candles with a

mean length of 15cm and a standard deviation of 0.10cm. A random sample of 49

candles is taken from each machine. Let x 虅1鈭抶 虅2 be the

difference (Machine 1 鈥� Machine 2) in the sample mean length of candles. Describe the

shape, center, and variability of the sampling distribution of x 虅1鈭抶 虅2.

Short Answer

Expert verified

Shape: Shape is approximately normal

Center: 渭x 虅1鈭抶 虅2=0

Variability:蟽x 虅1鈭抶 虅2=0.026cm

Step by step solution

01

Step 1:Given Information

We have been given that,

Machine 1 :

candles with a mean length,x1= 15cm

candles with a standard deviation,蟽1= 0.15cm

random sample of candles (n1)=49

Machine 2:

candles with a mean length,x2= 15cm

candles with a standard deviation,蟽2= 0.10cm

random sample of candles (n2)=49

02

Step 2:Explanation

n1 >30 and n2 >30

So, x 虅1鈭抶 虅2 has approximately normal shape.

渭x1鈭�x2=x1-x2=15-15=0

So,center =0

Variability:

localid="1654269722311" 蟽x1-x2=蟽12n1+蟽22n2=localid="1654269775856" 0.15249+0.10249=localid="1654269783223" 0.026cm

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Most popular questions from this chapter

Are teenagers going deaf? In a study of 3000randomly selected teenagers in 1990,450showed some hearing loss. In a similar study of 1800 teenagers reported in 2010,351showed some hearing loss.

a. Do these data give convincing evidence that the proportion of all teens with hearing

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b. Interpret the P-value from part (a) in the context of this study.

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