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Nadusha1986 [10]
3 years ago
6

An automobile manufacturer claims that its car has a 35.935.9 miles/gallon (MPG) rating. An independent testing firm has been co

ntracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 220220 cars, they found a mean MPG of 35.635.6. Assume the standard deviation is known to be 2.22.2. A level of significance of 0.020.02 will be used. Make a decision to reject or fail to reject the null hypothesis.
Mathematics
1 answer:
Serjik [45]3 years ago
5 0
<h2>Answer with explanation:</h2>

Let \mu be the population mean.

For the given claim , we have

Null hypothesis : H_0: \mu=35.9

Alternative hypothesis :  H_a: \mu\neq35.9

Since alternative hypothesis is two-tailed , so the test is a two-tailed test.

Given : Sample size : n=220  ;

Sample mean: \overline{x}=35.6  ;

Standard deviation: s=2.2

Test statistic for population mean:

z=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}

z=\dfrac{35.6-35.9}{\dfrac{2.2}{\sqrt{220}}}\approx-2.02

By using the standard normal distribution table of z , we have

P-value ( two tailed test ) : 2P(Z>|z|)=2(1-P(Z

=2(1-P(z

Since , the P-value is greater than the significance level of \alpha=0.02 , it means we do not have sufficient evidence to reject the null hypothesis.

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Assume the general population gets an average of 7 hours of sleep per night. You randomly select 45 college students and survey
tekilochka [14]

Answer:

a) ii. This is a left-tailed test.

b) -1.59

c) -1.301

d) i. reject null hypothesis

e) Option i) The data supports the claim that college students get less sleep than the general population.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 7 hours

Sample mean, \bar{x} = 6.87 hours

Sample size, n = 45

Alpha, α = 0.10

Sample standard deviation, s =  0.55 hours

First, we design the null and the alternate hypothesis

H_{0}: \mu = 7\text{ hours}\\H_A: \mu < 7\text{ hours}

a) We use one-tailed(left) t test to perform this hypothesis.

b) Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{6.87 - 7}{\frac{0.55}{\sqrt{45}} } =-1.59

c) Now,

t_{critical} \text{ at 0.10 level of significance, 44 degree of freedom } = -1.301

Since,                    

t_{stat} < t_{critical}

d) We fail to accept the null hypothesis and reject it.

We accept the alternate hypothesis and conclude that  mean number of hours of sleep for all college students is less than 7 hours.

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A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
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Step-by-step explanation:

<h3>Need to FinD :</h3>

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\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

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Angle sum property,

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\rule{200}{3}

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∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

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∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

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Hence , Proved

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