A research study was conducted about gender differences in "sexting." The researcher believed that the proportion of girls involved in "sexting" is less than the proportion of boys involved. The data collected in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States is out of 2231 males, 183 particpated in sexting. Out of 2169, 156 particpated. Is the proportion of girls sending sexts less than the proportion of boys "sexting?" Test at a 1% level of significance. a) If we use B to denote the boys and G to denote the girls, identify the correct alternative hypothesis. H₁: PB PG O H₁: PB PG OH₁: PB > PG b) Determine the test statistic. Round to two decimals. z = 1.26 c) Find the p-value and round to 4 decimals. p= d) Make a decision.
A research study was conducted about gender differences in "sexting." The researcher believed that the proportion of girls involved in "sexting" is less than the proportion of boys involved. The data collected in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States is out of 2231 males, 183 particpated in sexting. Out of 2169, 156 particpated. Is the proportion of girls sending sexts less than the proportion of boys "sexting?" Test at a 1% level of significance. a) If we use B to denote the boys and G to denote the girls, identify the correct alternative hypothesis. H₁: PB PG O H₁: PB PG OH₁: PB > PG b) Determine the test statistic. Round to two decimals. z = 1.26 c) Find the p-value and round to 4 decimals. p= d) Make a decision.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
Related questions
Question
![A research study was conducted about gender
differences in "sexting." The researcher believed that
the proportion of girls involved in "sexting" is less than
the proportion of boys involved. The data collected in
the spring of 2010 among a random sample of middle
and high school students in a large school district in the
southern United States is out of 2231 males, 183
particpated in sexting. Out of 2169, 156 particpated. Is
the proportion of girls sending sexts less than the
proportion of boys "sexting?" Test at a 1% level of
significance.
a) If we use B to denote the boys and G to denote the
girls, identify the correct alternative hypothesis.
b) Determine the test statistic. Round to two decimals.
Z =
OH₁: PB < PG
O H₁: PB PG
OH₁: PB > PG
p=
1.26
c) Find the p-value and round to 4 decimals.
d) Make a decision.
O Reject the null hypothesis
● Fail to reject the null hypothesis
e) Write the conclusion.
There is not sufficient evidence to support the
claim that the proportion of girls who sext is less
than boys.
There is sufficient evidence to support the claim
that the proportion of girls who sext is less than
boys.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fe45194-e1a9-4901-b715-7f22cd2e7bb2%2F97a1445c-b168-4ccd-a0ba-2db8af17b379%2F4i2mmoc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A research study was conducted about gender
differences in "sexting." The researcher believed that
the proportion of girls involved in "sexting" is less than
the proportion of boys involved. The data collected in
the spring of 2010 among a random sample of middle
and high school students in a large school district in the
southern United States is out of 2231 males, 183
particpated in sexting. Out of 2169, 156 particpated. Is
the proportion of girls sending sexts less than the
proportion of boys "sexting?" Test at a 1% level of
significance.
a) If we use B to denote the boys and G to denote the
girls, identify the correct alternative hypothesis.
b) Determine the test statistic. Round to two decimals.
Z =
OH₁: PB < PG
O H₁: PB PG
OH₁: PB > PG
p=
1.26
c) Find the p-value and round to 4 decimals.
d) Make a decision.
O Reject the null hypothesis
● Fail to reject the null hypothesis
e) Write the conclusion.
There is not sufficient evidence to support the
claim that the proportion of girls who sext is less
than boys.
There is sufficient evidence to support the claim
that the proportion of girls who sext is less than
boys.
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