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An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From pre

melamori03 [73]

Answer:

We conclude that a compact microwave oven consumes a mean of more than 250 W.

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let $\mu$ = mean power consumption for microwave ovens.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 250 W {means that a compact microwave oven consumes a mean of no more than 250 W}

Alternate Hypothesis, $H_A$ : $\mu$ > 250 W {means that a compact microwave oven consumes a mean of more than 250 W}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean power consumption for ovens = 257.3 W

σ = population standard deviation = 15 W

n = sample of microwave ovens = 20

So, the test statistics = $\frac{257.3-250}{\frac{15}{\sqrt{20} } }$

= 2.176

The value of z test statistics is 2.176.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.

7 0

3 years ago

An arrow is shot vertically upward from a platform 16ft high at a rate of 190ft/sec. When will the arrow hit the ground?

natta225 [31]

Answer:

time required for arrow to reach ground is 10.8 sec

when t = 10.8 seconds to the nearest tenth

Step-by-step explanation:

Given values are

Velocity = 190 ft/sec height = 16 ft

Given formula is

h=−16t²+vt+h0

adding the values, we get

h(t)= -16t²+190t+16

so we have to find when the hit he ground, so at ground the height will be 0

0= -16t²+190t+16

-16t²² + 190t + 16= 0

using the quadratic formula

x = (-b +(b2 - 4ac)1/2)/2a

values

a = -16, b = 190, c = 16

x= -190 + ((-190)²- 4 (-16)(16) ½ / 2(-16)

x= -190 + ((-190) ²+1024) ½ / 2(-16)

x= -190+ (-190²+ 32²) ½ /-32

taking under root

x= -190 + ( -190+32)/ -32

x= 190 + (-158)/-32

we have 2 options,

x= 190 + (-158)/-32 x= 190 - (-158)/-32

x= 190 -158)/-32 x= 190 +158)/-32

x= -1 x= 10.875

or t = 10.875

so the negative root has no practical significance

and we have t = 10.8 seconds to the nearest tenth

4 0

3 years ago

Adam invested $12,000 in a six-year CD that paid 7.1% interest, but later needed to withdraw $2,500 early. If the CD’s penalty f

grigory [225]

The question is asking to choose among the following choices states the value of penalty that Adam would have if the CD's penalty for early withdrawals was eighteen months' worth of interest on the amount width drawn, and base on my calculation, the possible answer would be letter C. $266.25

4 0

3 years ago

Read 2 more answers

What is the minimum value for y= 3cosx?

VashaNatasha [74]

Take the deritive
y'=-3sinx
find whre it equals 0
it equals 0 at -pi, 0, pi, etc
find whre it changes from negative to positive
at -0.5pi, the derivitive is positive
at 0.5pi, the deritivie is negative
changes from positive to negative at x=0
that means that the max values are at pi and -pi in 2pi intervals

-pi, pi, 3pi, 5pi,etc
the min y value is -3

so the minimum(s) are/is at (2aπ,-3) where 'a' is an integer

8 0

3 years ago

"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing "Wrinkle recovery angle" measur

ludmilkaskok [199]

Answer:

At 5% there is significant evidence to reject the null hypothesis. You can conclude that there is a difference between the population mean of the wrinkle recovery angle of fabric treated with Permafresh and the population mean of the wrinkle recovery angle of fabric treated with Hylite.

a)

X[bar]₁= 120.8 degrees

X[bar]₂= 162.75 degrees

b)

S₁²= 14.5155 degrees

S₂²= 24.4727 degrees

Step-by-step explanation:

Hello!

The study variable is X: wrinkle recovery angle for a fabric specimen.

There is a suspicion that there is a difference in recovery from wrinkles after washing between two products (Permafresh and Hilite). To test this suspicion two random samples of fabric, 5 were treated with Permafresh and 4 were treated with Hylite resulting in the data:

Sample 1 (Permafresh)

X₁: wrinkle recovery angle for a fabric specimen treated with Permafresh.

X₁~N(μ₁;σ₁²)

n₁= 5

124; 104; 142; 111; 123

Sample mean X[bar]₁= (∑x₁i)/n₁= 604/5= 120.8 degrees

Sample variance S₁²= $\frac{1}{(n₁-1)}$ [(∑x₁²i)-(∑x₁i)²/n₁] = $\frac{1}{4}$ [(73806)-(604)²/5]= 210.7 degrees²

S₁= 14.515 ≅ 14.52 degrees

Sample 2 (Hylite)

X₂: wrinkle recovery angre for a fabric specimen trated with Hylite.

X₂~N(μ₂;σ₂²)

n₂= 4

147; 199; 149; 156

Sample mean X[bar]₂= (∑x₂i)/n₂= 651/4= 162.75 degrees

Sample variance S₂²= $\frac{1}{(n₂-1)}$ [(∑x₂²i)-(∑x₂i)²/n₂] = $\frac{1}{3}$ [(107747)-(651)²/4]= 598.916 ≅ 598.92 degrees²

S₂= 24.472≅ 24.47 degrees

To test the suspicion that there is a difference between the winkle recovery angle on fabric samples treated with Permafresh and Hylite, the hypothesis is:

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α: 0.05

To test the difference between the population means, considering that only sample information is available and the size of both samples, the most appropriate statistic to use is a pooled t for independent samples (unknown but equal population variances):

t= (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) ~t $_{n_1+n_2-2}$

Sa√(1/n₁+1/n₂)

Sa²= (n₁-1)S₁² + (n₂-1)S₂² = (4*210.7)+(3*598.92) = 377.08

n₁ + n₂ - 2 5+4-2

Sa= 19.418≅ 19.42

t= (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) = (120.8-162.75) - 0 = -3.22

Sa√(1/n₁+1/n₂) 19.42√(1/5+1/4)

Using the critical region approach, this rejection region is two-tailed with critical values:

$t_{n_1+n_2-2; \alpha/2 } = t_{7; 0.025 } = -2.365$

$t_{n_1+n_2-2; 1- \alpha/2 } = t_{7; 0.975 } = 2.365$

If t ≤ -2.365 or t ≥2.365, then the decision is to reject the null hypothesis.

If -2.365 < t < 2.365, then the decision is to not reject the null hypothesis.

Since the calculated t-value is less than the left critical value, the decision is to reject the null hypothesis.

I've calculated the p-value for the test: 0.0146

This p-value is less than the significance level of 0.05, then, using this approach, the decision is also to reject the null hypothesis.

This means, that at 5% there is significant evidence to reject the null hypothesis. You can conclude that there is a difference between the population mean of the wrinkle recovery angle of fabric treated with Permafresh and the population mean of the wrinkle recovery angle of fabric treated with Hylite.

I hope it helps!

4 0

4 years ago