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An electronic retailer believes that, at most 40% of their cellphone inventory was sold during November. The retailer surveyed 80 dealers and found that 38% of the inventory was sold. Since 38% less than 40%, is the difference of 2 percentage points sampling error or a significant difference? Test at .05 level.

Respuesta :

Answer:

The difference of 2 percentage points may be due to sampling error

Step-by-step explanation:

Given that an electronic retailer believes that, at most 40% of their cellphone inventory was sold during November.

Sample size n =80

Sample proportion p = 0.38

[tex]H_0: p=0.40\\H_a: p <0.40[/tex]

(left tailed test at 5% level)

p difference = -0.02

Assuming H0 to be true std error

= [tex]\sqrt{\frac{pq}{n} } \\=0.0548[/tex]

Z statistic = p diff/std error = -0.365

p value = 0.3575

Since p >0.05 we accept H0.

The difference of 2 percentage points may be due to sampling error

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