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Nonamiya [84]
3 years ago
15

The mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that

the smoking age has significantly changed since the invention of ENDS—electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of 30 smokers found that their mean starting age was 12.2 years old. Do the data support the claim at the 5% significance level?
What are the correct hypotheses?
H0:
H1:
Based on the hypotheses, find the following:
Test Statistic z = (Give answer to at least 4 decimal places)
Critical Values =± (Give answer to at least 4 decimal places)
Based on the above we choose to .....

a. Reject the null hypothesis
b. Accept the null hypothesis
c. Fail to reject the null hypothesis

The correct summary would be:

a. There is enough evidence to reject the claim
b. There is not enough evidence to reject the claim
c. There is enough evidence to support the claim
Mathematics
1 answer:
lakkis [162]3 years ago
6 0

Answer:

Null hypothesis:\mu = 13  

Alternative hypothesis:\mu \neq 13

z=\frac{12.2-13}{\frac{2}{\sqrt{30}}}=-2.191  

a. Reject the null hypothesis

c. There is enough evidence to support the claim

Step-by-step explanation:

Data given and notation  

\bar X=12/2 represent the sample mean  

s=20000 represent the standard deviation for the sample  

\sigma =2 represent the population standard deviation

n=30 sample size  

\mu_o =13 represent the value that we want to test  

\alpha=0.05 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the smoking age has significantly changed since the invention of ENDS—electronic nicotine delivery systems, the system of hypothesis would be:  

Null hypothesis:\mu = 13  

Alternative hypothesis:\mu \neq 13

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

z=\frac{12.2-13}{\frac{2}{\sqrt{30}}}=-2.191  

What do you conclude? Using the p-value approach  

Since is a two tailed test the p value would be:  

p_v =2*P(Z  

Since the p_v then the correct decision is:

a. Reject the null hypothesis

And the best conclusion is :

c. There is enough evidence to support the claim

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Triss [41]

The value of the given expression is \frac{-13}{20}.

Solution:

Given expression is \frac{3}{4} \times3\frac{2}{5}-\frac{5}{5}.

Let us first convert mixed fraction into improper fraction.

3\frac{2}{5}=\frac{(3\times5)+2}{5}=\frac{17}{5}

Substitute this in the given expression.

\frac{3}{4} \times3\frac{2}{5}-\frac{5}{5}=\frac{3}{4} \times\frac{7}{15}-\frac{5}{5}

                  =\frac{21}{60}-\frac{5}{5}

To simplify the above expression, 21 and 60 are cancelled by 3.

                 =\frac{7}{20}-\frac{1}{1}

Do cross multiplication to make the denominator same.

                 =\frac{7}{20}-\frac{20}{20}

                 =\frac{7-20}{20}

                 =\frac{-13}{20}

The value of the given expression is \frac{-13}{20}.

7 0
3 years ago
Solve the system.
liraira [26]

Answer:

Option D is right,.

Step-by-step explanation:

-a+4b+2c=-8   ... i

3a+b-4c=9      ... ii

b=-1                 ... iii

Substitute the value of b, in i and ii

-a-4+2c =-8 or -a+2c = -4

and 3a-1-4c = 9 or 3a -4c =8

Now we have two equations in two variables

-a+2c =-4 and 3a-4c =8

a = 2c+4:  substitute this in the other equatin.

3(2c+4)-4c =8 Or 2c +12 =8

2c =-4 or c = -2

Substitute in -a+2c =12

-a-2 = -4

a = -2+4 =2

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6 0
3 years ago
A flashlight battery manufacturer makes a model of battery whose mean shelf life is three years and four months, with a standard
Vladimir [108]

Answer:

17,065 of those batteries can be expected to last between three years and one month and three years and seven months

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem:

I will calculate the time in months. Each year has twelve months.

Mean shelf life is three years and four months, with a standard deviation of three months. So

\mu = 3*12 + 4 = 40

\sigma = 3

Proportion lasting between three years and one month and three years and seven months:

This is the pvalue of Z when X = 3*12 + 7 = 43 subtracted by the pvalue of Z when X = 3*12 + 1 = 37

X = 43

Z = \frac{X - \mu}{\sigma}

Z = \frac{43 - 40}{3}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 37

Z = \frac{X - \mu}{\sigma}

Z = \frac{37 - 40}{3}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6826

Out of 25,000 batteries:

68.26% of the batteries are expected to last between three years and one month and three years and seven months.

0.6826*25000 = 17,065

17,065 of those batteries can be expected to last between three years and one month and three years and seven months

6 0
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3A+2B-4A-2B=20-26

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