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moses638
25.12.2020 •
Mathematics
Wal-Mart conducted a study to check the accuracy of checkout scanners at its stores. At each of the 60 randomly selected Wal-Mart stores, 100 random items were scanned. The researchers found that 52 of the 60 stores had more than 2 items that were priced inaccurately (the national standards allow a maximum of 2 items out of 100 items priced accurately by the scanners). a) Construct a 95% confidence interval for proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned and give a practical interpretation of this interval. (3 Points) b) Wal-Mart claims that 99% of its stores comply with the national standard on accuracy of price scanners. Comment on the believability of Wal-Mart’s claim based on your results in part (a). (1 Point) c) Determine the number of Wal-Mart stores that must be sampled in order to estimate the true proportion to within 0.05 with 90% confidence. (3 Points)
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Ответ:
a
The 95% confidence interval is
Generally the interval above can interpreted as
There is 95% confidence that the true proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned lie within the interval
b
Generally 99% is outside the interval obtained in a above then the claim of Wal-mart is not believable
c
Step-by-step explanation:
From the question we are told that
The sample size is n = 60
The number of stores that had more than 2 items price incorrectly is k = 52
Generally the sample proportion is mathematically represented as
=>![\^ p = \frac{ 52 }{ 60 }](/tpl/images/1007/6465/0df93.png)
=>![\^ p = 0.867](/tpl/images/1007/6465/4af2e.png)
From the question we are told the confidence level is 95% , hence the level of significance is
=>![\alpha = 0.05](/tpl/images/1007/6465/246a1.png)
Generally from the normal distribution table the critical value of
is
Generally the margin of error is mathematically represented as
=>![E = 1.96 * \sqrt{\frac{ 0.867 (1- 0.867)}{60} }](/tpl/images/1007/6465/02ee5.png)
=>![E = 0.0859](/tpl/images/1007/6465/a84c5.png)
Generally 95% confidence interval is mathematically represented as
=>![0.867 - 0.0859 < p < 0.867 + 0.0859](/tpl/images/1007/6465/9e759.png)
=>![0.7811 < p < 0.9529](/tpl/images/1007/6465/9dd2d.png)
Generally the interval above can interpreted as
There is 95% confidence that the true proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned lie within the interval
Considering question b
Generally 99% is outside the interval obtained in a above then the claim of Wal-mart is not believable
Considering question c
From the question we are told that
The margin of error is E = 0.05
From the question we are told the confidence level is 95% , hence the level of significance is
=>![\alpha = 0.05](/tpl/images/1007/6465/246a1.png)
Generally from the normal distribution table the critical value of
is
Generally the sample size is mathematically represented as
=>![n= [\frac{1.645 }}{0.05} ]^2 * 0.867 (1 - 0.867 )](/tpl/images/1007/6465/4cc60.png)
=>
Ответ:
D
Step-by-step explanation:
If two secants intersect to form the vertex of an angle outside a circle and the sides of the angle intercept arcs on the circle, then the measure of the angle is equal to one-half the difference of the measures of the arcs intercepted by the sides of the angle.
So