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Semmy [17]
3 years ago
8

In an article in Marketing Science, Silk and Berndt investigate the output of advertising agencies. They describe ad agency outp

ut by finding the shares of dollar billing volume coming from various media categories such as network television, spot television, newspapers, radio, and so forth.Suppose that a random sample of 392 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.41 percent, and assume that alpha equals 1.43 percent. Calculate a 95 percent confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies.
Mathematics
1 answer:
fredd [130]3 years ago
7 0

Answer: (7.27%, 7.55%)

Step-by-step explanation:

As per given , we have

Sample size : n= 392

Sample mean : \overline{x}=7.41\%

\sigma=1.43\%

Critical two-tailed z-value for 95% confidence = z_{\alpha/2}=1.96

Required confidence interval would be :

7.41\%\pm (1.96)\dfrac{1.43\%}{\sqrt{392}}\\\\=7.41\%\pm 0.14\%\\\\=(7.27\%, 7.55\%)

Hence, the required 95% confidence interval for the mean percentage share of billing volume from network television for the population of all U.S. advertising agencies : (7.27%, 7.55%)

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Dahasolnce [82]

Answer:

1.  χ² = <u>  15.3902 </u>

2. The p value is :_____.a. less than .005

3.  Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

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Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the employee health insurance coverage is independent of the size of the company

against the claim

Ha: the employee health insurance coverage is not independent of the size of the company

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

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4) Computations:

Under H0 , the observed frequencies are :

Observed       Expected E        (O-E)         (O-E)²             (O-E)²/E

33                   42                      -9               81                    1.928  

68                  63                         5              25                  0.3968

88                  84                         4               16                  0.1904

17                    8                           9              81                  10.125

7                     12                          -5             21                    1.75

<u>12                    16                         -4              16                     1              </u>

<u>                                                                                           15.3902    </u>

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