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Eating Together In December 2001, 38% of adults with
Chapter , Problem 20AYU(choose chapter or problem)
Problem 20AYU
Problem
Eating Together In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Has the proportion of families with children under the age of 18 who eat dinner together 7 nights a week decreased? Use the α = 0.05 significance level.
Questions & Answers
QUESTION:
Problem 20AYU
Problem
Eating Together In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Has the proportion of families with children under the age of 18 who eat dinner together 7 nights a week decreased? Use the α = 0.05 significance level.
ANSWER:
Answer :
Step 1 of 2:
Given, 38% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together 7 nights a week and level of significance .
= 38% = 0.38 and 1 -
= 0.62
: p = 0.38
: p < 0.38
n = 1122, x = 403 and = 0.05
264.34 > 10
Let test statistic be
Z =
Where, p = x/n = 403/1122 = 0.359 , = 0.38 and 1 -
=0.62
then , Z =
Z =
= = -1.45
The critical value for left tailed test when =0.05 is -1.645
Hence, do not reject the null hypothesis