How many 1/2-pound portions of grapes are in 3/4 pound?

The diameters of bearings used in an aircraft landing gear assembly have a standard deviation of ???? = 0.0020 cm. A random samp

vovikov84 [41]

Answer:

(a) We conclude after testing that mean diameter is 8.2500 cm.

(b) P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) 95% confidence interval on the mean diameter = [8.2525 , 8.2545]

Step-by-step explanation:

We are given with the population standard deviation, $\sigma$ = 0.0020 cm

Sample Mean, Xbar = 8.2535 cm and Sample size, n = 15

(a) Let Null Hypothesis, $H_0$ : Mean Diameter, $\mu$ = 8.2500 cm

Alternate Hypothesis, $H_1$ : Mean Diameter, $\mu$ $\neq$ 8.2500 cm{Given two sided}

So, Test Statistics for testing this hypothesis is given by;

$\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ follows Standard Normal distribution

After putting each value, Test Statistics = $\frac{8.2535-8.2500}{\frac{0.0020}{\sqrt{15} } }$ = 6.778

Now we are given with the level of significance of 5% and at this level of significance our z score has a value of 1.96 as it is two sided alternative.

<em>Since our test statistics does not lie in the rejection region{value smaller than 1.96} as 6.778>1.96 so we have sufficient evidence to accept null hypothesis and conclude that the mean diameter is 8.2500 cm.</em>

(b) P-value is the exact % where test statistics lie.

For calculating P-value , our test statistics has a value of 6.778

So, P(Z > 6.778) = Since in the Z table the highest value for test statistics is given as 4.4172 and our test statistics has value higher than this so we conclude that P - value is smaller than 2 x 0.0005% { Here 2 is multiplied with the % value of 4.4172 because of two sided alternative hypothesis}

Hence P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) For constructing Two-sided confidence interval we know that:

Probability(-1.96 < N(0,1) < 1.96) = 0.95 { This indicates that at 5% level of significance our Z score will lie between area of -1.96 to 1.96.

P(-1.96 < $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96\frac{\sigma}{\sqrt{n} }$ < $Xbar - \mu$ < $1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

P( $-Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $-\mu$ < $1.96\frac{\sigma}{\sqrt{n} }-Xbar$ ) = 0.95

P( $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $\mu$ < $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

So, 95% confidence interval for $\mu$ = [ $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ , $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ]

= [ $8.2535-1.96\frac{0.0020}{\sqrt{15} }$ , $8.2535+1.96\frac{0.0020}{\sqrt{15} }$ ]

= [8.2525 , 8.2545]

Here $\mu$ = mean diameter.

Therefore, 95% two-sided confidence interval on the mean diameter

= [8.2525 , 8.2545] .

6 0

3 years ago

Read 2 more answers

Identify the biggest perfect square for 75

mr_godi [17]

Answer:

We just multiply 75 with 3 to make it a perfect square. This is because, 75 = 5 × 5 × 3. 3 doesn't have a pair. Thus 75 × 3 = 225 and √225 is 15.

Step-by-step explanation:

8 0

2 years ago

A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the ce

nika2105 [10]

It the wiper blade (and arm) made a full rotation, 2 circles would be formed.

One small circle with radius b, and a larger circle with radius a+b.

The areas of these 2 circles are respectively:

$\pi b^2=\pi\cdot 5^2=25 \pi (in^2)$ and

$\pi (a+b)^2=\pi (14+5)^2=361\pi (in^2)$

120° is 1/3 of a complete angle 360° which form a circle, so the areas formed by the arm of length b, and the arm + the wiper blade (a+b) are:

$\frac{25 \pi}{3}$ and $\frac{361\pi}{3}$ in squared respectively.

the actual wiped area is $\frac{361\pi}{3}-\frac{25 \pi}{3}= \frac{336\pi}{3}=112\pi \approx351.7$ (in squared)

Area of the window is 54*24= 1296 (in squared)

thus, the ratio of the wiped area to the whole area of the window is 351.7/1296=0.271

Converted to percentages, this is 27.1%

Answer: 27.1%

3 0

3 years ago

What is the radical expression that is equivalent to the expression

puteri [66]

Hello from MrBillDoesMath!

Answer:

fourthroot(35)

Discussion:

The question is a bit unclear as to the desired answer.... but here goes!

(35)^1/4 is the fourth root of 35, that is, symbolically, fourthroot(35).

Note the fourth root of a number is the same as the square root of the square root of the number.

Regards,

MrB

P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

6 0

3 years ago

Helppppppppplppppppp

irinina [24]

Answer:

number 1 is 2 number 2 is 15 number 4 is 30

Step-by-step explanation:

6 0

3 years ago