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Amiraneli [1.4K]
3 years ago
12

Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical fact

or in determining the likelihood of an accident occurring (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)2. On a heavily traveled highway, a random sample of 55 cars revealed a mean and a variance of speeds of 62.5 mph and 94.7(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)
1. Set up the competing hypothesis to test wxpert,s claim.
2. At the 5% significance level find the critical value and state the decision rule.
3. Can you conclude that driving conditions are dangerous on this highway? explain.
Mathematics
1 answer:
scZoUnD [109]3 years ago
7 0

Answer:

Explained below.

Step-by-step explanation:

The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².

(1)

The hypothesis for both the test can be defined as:

<em>H</em>₀: The variance of speeds does not exceeds 75 (mph)², i.e. <em>σ</em>² ≤ 75.

<em>Hₐ</em>: The variance of speeds exceeds 75 (mph)², i.e. <em>σ</em>² > 75.

(2)

A Chi-square test will be used to perform the test.

The significance level of the test is, <em>α</em> = 0.05.

The degrees of freedom of the test is,

df = n - 1 = 55 - 1 = 54

Compute the critical value as follows:

\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153

Decision rule:

If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.

(3)

Compute the test statistic as follows:

\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}

    =\frac{(55-1)\times 94.7}{75}\\\\=68.184

The test statistic value is, 68.184.

Decision:

cal.\chi^{2}=68.184

The null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.

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Boyd grows only tomatoes and raspberries in his garden. Last year, he grew 140 pounds of tomatoes and 60 pounds of raspberries.
nadya68 [22]

Answer:

29%.

Step-by-step explanation:

We have been given that Boyd grew 140 pounds of tomatoes and 60 pounds of raspberries. This year, the production, by weight, of tomatoes declined by 20 percent, and the production, be weight, of raspberries declined by 50 percent.

First of all, we will find the weight of tomatoes and raspberries using the given information.

Since the production, by weight, of tomatoes declined by 20 percent, so this year production of tomatoes is 80% of 140 pounds.

\frac{80}{100}\times 140=0.80\times 140=112

Since the production, be weight, of raspberries declined by 50 percent, so this year production of raspberries is 50% of 30 pounds.

\frac{50}{100}\times 60=0.50\times 60=30

Total production this year: 112+30=142 pounds.

Now, we will percent decrease formula.

\text{Percent decrease}=\frac{\text{Initial value-Final value}}{\text{Initial value}}\times 100

\text{Percent decrease}=\frac{(140+60)-142}{140+60}\times 100

\text{Percent decrease}=\frac{(200)-142}{200}\times 100

\text{Percent decrease}=\frac{58}{200}\times 100

\text{Percent decrease}=0.29\times 100

\text{Percent decrease}=29

Therefore, the total yield, by weight, of Boyd's garden declined by 29%.

5 0
3 years ago
15 - 5 x = 10 x + 45
Tomtit [17]

Answer:

x=-2

Step-by-step explanation:

add 5x , then subtract 45, then divide by 15

6 0
3 years ago
Read 2 more answers
Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.
Serga [27]

Answer:

<h3>The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequences</h3>

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

2/r²+2/r = 24

(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

r = -1/4 0r 1/3

Since a= 2/r then a = 2/(-1/4)or  a = 2/(1/3)

a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of  a geometric sequence is expressed as

if r = -1/4 and a = -8

Tn = -8(-1/4)^(n-1)

if r = 1/3 and a = 6

Tn = 6(1/3)^(n-1)

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

6 0
3 years ago
IM DESPERATE
telo118 [61]
You can scan it on brainly, It’ll help you
7 0
2 years ago
If f ( x ) = 1 3 x − 5 , what is f ( − 6 ) ?
RoseWind [281]

Answer:

-4

Step-by-step explanation:

by finding the exact value.

6 0
3 years ago
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