Question

first picture is the information

2-) In a survey of 1000 U.S. teen. 372 said that they own smartphones. Find a point estimate for the population proportion of U.S. teens who own smartphones

Answer 1

X represents the number of people having an own smartphone in the sample. The sample proportion is p̂ (called "p-hat"), and it is computed by taking the ratio of the number of successes in the sample to the sample size, that is:

  $equation_image183.gif$

If there are more than 5 successes and more than 5 failures, then the confidence interval can be computed with this formula:

  $equation_image114.gif$

where Z is the Z-value at 90% level of significance. so , Z = 1.645

According to the question   $\hat{p}$ = 372 / 1000 = 0.372

Now 90% confidence interval for population proportion is  $equation_image114.gif$

= ( 0.372 - {1.645 *$\sqrt$(0.372(1-0.372) /1000) } , 0.372 + {1.645 *$\sqrt$(0.372(1-0.372) /1000) } )

= ( 0.372 - 0.0251 , 0.372+0.0251 )

= ( 0.3469 , 0.3971)