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deff fn [24]
3 years ago
13

Carter Motor Company claims that its old sedan, the Libra, would average less than 19 miles per gallon in the city. Assuming tha

t a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
Mathematics
1 answer:
topjm [15]3 years ago
7 0

Answer:

Null hypothesis: \mu \geq 19

Alternative hypothesis: \mu < 19

For this case after conduct the hypothesis test they conclude that that the conclusion is to reject the null hypothesis.

So then we can conclude that the true mean for this case is likely to be lower than 19 miles per gallon at some significance level who represent the error that can be present in this conclusion

Step-by-step explanation:

When we conduct and hypothesis test the first step is find the system of hypothesis based on the claim.

For this case the objective is test the claim that the average less than 19 miles per gallon in the city (alternative hypothesis) and the complement should be the null hypothesis so then the system of hypothesis are:

Null hypothesis: \mu \geq 19

Alternative hypothesis: \mu < 19

For this case after conduct the hypothesis test they conclude that that the conclusion is to reject the null hypothesis.

So then we can conclude that the true mean for this case is likely to be lower than 19 miles per gallon at some significance level who represent the error that can be present in this conclusion

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Answer:

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3 years ago
Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technolog
lara31 [8.8K]

Answer:

SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048

If we replace the values obtained we got:

0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257

0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443

The 95% confidence interval would be given by (0.257;0.443)

Step-by-step explanation:

Notation and definitions

X=35 number of people that agree.

n=100 random sample taken

\hat p=\frac{35}{100}=0.35 estimated proportion of people that agree

p true population proportion of peopl that agree

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

The standard error is given by:

SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048

If we replace the values obtained we got:

0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257

0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443

The 95% confidence interval would be given by (0.257;0.443)

6 0
3 years ago
Read 2 more answers
A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these
Vinvika [58]

Answer:

133 fishes

Step-by-step explanation:

Units of food A = 400 units

Units of food B = 400 units

Fish Bass required 2 units of A and 4 units of B.

Fish Trout requires 5 units of A and 2 units of B.

i. For food A,

total units of food A required = 2 + 5

                                                 = 7 units

number of bass and trout that would consume food A = 2 x \frac{400}{7}

                                               = 114.3

number of bass and trout that would consume food A = 114

ii. For food B,

total units of food B required = 4 + 2

                                                = 6 units

number of bass and trout that would consume food B = 2 x \frac{400}{6}

                                                 = 133.3

number of bass and trout that would consume food B = 133

Thus, the maximum number of fish that the lake can support is 133.

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The answer I got is (-6,-2) the x value is -6
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