Question

Do you have an insatiable craving for chocolate or some other food? since many north americans apparently do, psychologists are designing scientific studies to examine the phenomenon. According to the survey, it was revealed that 97% of the women in the study acknowledged specific food cravings while only 67% of the men did. Assume that 600 of the respondents were women and 400 were men. Find and interpret the 90% confidence interval for the difference between the population proportions.

Answer 1

A confidence interval for the difference between the population proportions = ( .2597 , .3403 )

Confidence interval mean

Estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

In statistics, a claim to 95% confidence simply means that the researcher has seen one possible interval from a large number of possible ones, from which 19 out of 20 intervals contain the true value of the parameter.

If repeat the test, can expect your estimate to fall between these numbers with a reasonable degree of certainty.

In statistics, confidence is another probability word.

β₁ = x₁/n₁  = 582/600 = 0.97

β₂ = x₂/n₂ = 268/400 = 0.67

( β₁ - β₂) ± z √β₁( 1 -β₁ )/n₁ + β₂(1 - β₂)/n₂

          = (.97 - .67 ) ± 1.645 √.97( 1 - .97)/600 + .97( 1 - .67)/400

          = .30 ± 0.4336

         = ( .2597 , .3403 )

A confidence interval for the difference between the population proportions = ( .2597 , .3403 )

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