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sammy [17]
3 years ago
10

A survey by American Express Spending reported that the average amount spent on a wedding gift for a close family member is $166

. A random sample of 45 people who purchased wedding gifts for a close family member spent an average of $160.50. Assume that the population standard deviation is $38. Use a 95% confidence interval to test the validity of this report and choose the one statement that is correct.
a. Because this confidence interval does include $166, the report by American Express Spending is not validated.
b. Because this confidence interval does include $166, the report by American Express Spending is validated.
c. Because this confidence interval does not include $166, the report by American Express Spending is not validated.
d. Because this confidence interval does not include $166, the report by American Express Spending is validated.
Mathematics
1 answer:
Marysya12 [62]3 years ago
5 0
It would be B !!


Sshajsnsbshsbsor idk
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An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviatio
Lena [83]

Answer:

The  width is  w = \$ 729.7

Step-by-step explanation:

From the question we are told that

   The population standard deviation is  \sigma =  \% 1,000

    The  sample size is  n  = 50

    The sample mean  is  \= x  =  \$ 15,000

Given that the confidence level is  99% then the level of significance is mathematically represented as  

               \alpha  =  100 - 99

=>            \alpha  =  1\%

=>             \alpha  = 0.01

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table, the value is

             Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } =  2.58

Generally margin of error is mathematically represented as

             E =  Z_{\frac{\alpha }{2} *  \frac{\sigma }{\sqrt{n} }

substituting values

              E = 2.58 *  \frac{1000 }{\sqrt{50} }

              E = 2.58 *  \frac{1000 }{\sqrt{50} }

               E = 364.9

The width of the 99% confidence interval is mathematically evaluated as

         w = 2 * E

substituting values

          w = 2 * 364.9

          w = \$ 729.7

5 0
2 years ago
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