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jeyben [28]
3 years ago
11

A newspaper poll asked respondents if they trusted "eco friendly" labels on cleaning products. Out of 1000 adults surveyed, 498

responded "yes." We would like to test if the proportion of respondents that trust these labels is at least 50%. The calculated test statistic value is
Mathematics
1 answer:
Paul [167]3 years ago
7 0

Answer:

So the p value obtained was a very high value and using the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of respondents that trust these labels is not significanlty less than 0.5 or 50%.  

Step-by-step explanation:

1) Data given and notation

n=1000 represent the random sample taken

X=498 represent the adults that trust these labels

\hat p=\frac{498}{1000}=0.498 estimated proportion of respondents that trust these labels

p_o=0.5 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of respondents that trust these labels is at least 50%:  

Null hypothesis:p\geq 0.5  

Alternative hypothesis:p < 0.5  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.498 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-0.126  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level is not provided but we can assume it as \alpha=0.05. The next step would be calculate the p value for this test.  

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

p_v =P(Z  

So the p value obtained was a very high value and using the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of respondents that trust these labels is not significanlty less than 0.5 or 50%.  

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Shalnov [3]

Answer:

The surface area of the figure = 962 ft²

Step-by-step explanation:

The rectangle dimensions and its area given below

Dimensions       Number         Area

12 x 7                2                   12 x 7 x 2 = 168

16 x 7                1                    16 x 7 = 112

12 x (16 + 5)     1                    12 x 21 = 252

16 x 12              1                    16 x 12 = 192

16 x 13              1                     16 x 13 = 208

Triangle dimensions

Dimensions           Number         Area

b = 12  & h = 5       2                bh/2 = (12*5)/2  = 30

To find total area

Total area = 168 + 112 + 252 + 192 + 208 + 30 = 962 ft²

5 0
3 years ago
predict the attendance for minor league baseball in the year 2005. a. 5,208,000 b. 4,495,000 c. 44,950,000 d. 52,080,000
solong [7]

Answer:

c. 44,950,000

Step-by-step explanation:

The following table is missing:

Year   Attendance (millions)  

1985   18.4  

1990   25.2  

1995   33.1  

2000  37.6  

Using a calculator, the line of best fit is obtained. Equation:

y = 1.31x - 2581.6

where y is attendance (in millions)  and <em>x</em> is the year. Replacing with x = 2005 into the equation, we get:

y = 1.31(2005) - 2581.6

y = 44.95 millions or 44,950,000

6 0
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Answer:

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100 - 10 = 3x

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3 years ago
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