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aleksley [76]
3 years ago
10

Suppose the number of free throws in a basketball game by one player are normally distributed with a standard deviation 0.97 fre

e throws. A random sample of basketball players from the population produces a sample mean of x¯=4.9 free throws. What value of z should be used to calculate a confidence interval with a 95% confidence level? 20.10 1.282 20.05 1.645 0.025 1.960 20.005 2.576 2.326
Mathematics
1 answer:
babunello [35]3 years ago
3 0

Answer: 1.960

Step-by-step explanation:

The value of z we use to calculate a confidence interval with a (1-\alpha) confidence level is a two-tailed test value i.e. represented by :-

              z_{\alpha/2}

Given : The level of confidence: 1-\alpha=0.95

Then, significance level : \alpha: 1-0.95=0.05

With the help of standard normal distribution table for z , we have

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.960

Hence, the value of z should be used to calculate a confidence interval with a 95% confidence level =1.960

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13 + 7 × (8 - 3)
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6 0
3 years ago
The difference between an observational study and an experiment is that:
yulyashka [42]

Answer:

B

Step-by-step explanation:

An experiment is a study carried out in a controlled environment where the person undertaking the research hopes to understand cause and effect between the independent and dependent variables. An example of a experiment is the palovian experiment

The independent variable is the variable that the person carrying out an experiment changes or manipulates. the independent variable usually have a direct effect on the dependent variable

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable

Observational study is the study where the researcher observes and measures cause and effect between independent and dependent variables without trying  to control or influence the population

4 0
2 years ago
A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines
storchak [24]

Answer:

The null hypothesis is H_o: \mu = 4.

The alternate hypothesis is H_a: \mu \neq 4

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

H_o: \mu = 4

At the alternate hypothesis we test if it is different. So

H_a: \mu \neq 4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

4 is tested at the null hypothesis:

This means that \mu = 4

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that n = 196, X = 4.14

He knows that the population standard deviation is 0.83 cm.

This means that \sigma = 0.83

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}

z = 2.36

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

5 0
2 years ago
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Pavel [41]

Answer:

$149

Step-by-step explanation:

He spent 55 on sneakers at first, then he recieved 30 more, and gave 20 to the mom, which i added to the equation, and what he has left i also added.  

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$5,000 is invested at a rate of 7% compounded monthly. Determine the final balance after 5 years.
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Answer:11,256

Step-by-step explanation:

4 0
2 years ago
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