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Number of Text Messages a Day A random sample of n = 755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages,32 with standard error about 6.1. State the population and parameter of interest. Use the information from the sample to give the best estimate of the population parameter. Find and interpret a 95% confidence interval for the mean number of text messages.

Respuesta :

Answer:

The 95% confidence interval is  (29.54 - 53.46}

Step-by-step explanation:

given data:

[tex]\hat X = 41.5[/tex]

Se = 6.1

n = 755

a) best estimate  [tex]\hat x = 41.5[/tex]

b) at 95% confidence interval

[tex]\alpha = 1- 0.95 = 0.05[/tex]

[tex]\alpha /2 = 0.025[/tex]

[tex]z_{\alpha/2} = z_{0.025} = 1.96[/tex]

at 95% confidence interval for [/tex]\mu[/tex]

[tex]\hat x \pm z_{\alpha /2} \times Se[/tex]

[tex]41.5 \pm 1.96\times 6.1[/tex]

[tex]41.5 \pm 11.96[/tex]

The 95% confidence interval is  (29.54 - 53.46}

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