Question

Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females the following question: "Are you annoyed by people who repeatedly check their mobile phones while having an in-person conversation?" Among the 539 males surveyed, 188 responded "Yes"; among the 588 females surveyed, 219 responded "Yes." Does the evidence suggest a higher proportion of females are annoyed by this behavior? Complete parts (a) through (g) below. (a) Determine the sample proportion for each sample. The proportions of the females and males who took the survey and are annoyed by the behavior in question are 0.3732 and 0.3480, respectively. (Round to four decimal places as needed.) (b) Explain why this study can be analyzed using the methods for conducting a hypothesis test regarding two independent proportions. Select all that apply. n1p1(1-p1)≥10 and n2p2(1-p2)≥10 The samples are independent. (c) What are the null and alternative hypotheses? Let p1 represent the population proportion of females who are annoyed by the behavior in question and p2 represent the population proportion of males who are annoyed by the behavior in question. H0: p1 = p2 H1: p1 > p2 (d) Describe the sampling distribution of pfemale-pmale. Draw a normal model with the area representing the P-value shaded for this hypothesis test. The sampling distribution is approximately normal with mean 0 and standard deviation 0.0252. (Type an integer or decimal rounded to four decimal places as needed.) Draw a normal model with the area representing the P-value shaded for this hypothesis test. Choose the correct graph below, where the horizontal axis represents pfemale-pmale. A normal curve is over a horizontal axis and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 0.0236. The area under the curve and to the right of the vertical line segment is shaded. (e) Determine the P-value based on the model from part (d). First find the test statistic for this hypothesis test. 0.94 (Round to two decimal places as needed.) Determine the P-value for this hypothesis test. 0.174 (Round to three decimal places as needed.) (f) Interpret the P-value. If the population proportions are equal, one would expect a sample difference proportion greater than or equal to 0.0252 in about 174 out of 1000 repetitions of this experiment. (Round to the nearest integer as needed.) (g) Based on the P-value, what does the sample evidence suggest? That is, what is the conclusion of the hypothesis test? Assume an α=0.05 level of significance. Do not reject H0. There is not sufficient evidence at the α=0.05 level of significance to suggest a higher proportion of females are annoyed by the behavior in question.

Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females the following question: "Are you annoyed by people who repeatedly check their mobile phones while having an in-person conversation?" Among the 539 males surveyed, 188 responded "Yes"; among the 588 females surveyed, 219 responded "Yes." Does the evidence suggest a higher proportion of females are annoyed by this behavior? Complete parts (a) through (g) below.

(a) Determine the sample proportion for each sample.
The proportions of the females and males who took the survey and are annoyed by the behavior in question are 0.3732 and 0.3480, respectively.
(Round to four decimal places as needed.)

(b) Explain why this study can be analyzed using the methods for conducting a hypothesis test regarding two independent proportions. Select all that apply.
n1p1(1-p1)≥10 and n2p2(1-p2)≥10
The samples are independent.

(c) What are the null and alternative hypotheses? Let p1 represent the population proportion of females who are annoyed by the behavior in question and p2 represent the population proportion of males who are annoyed by the behavior in question.
H0: p1 = p2
H1: p1 > p2

(d) Describe the sampling distribution of pfemale-pmale. Draw a normal model with the area representing the P-value shaded for this hypothesis test.
The sampling distribution is approximately normal with mean 0 and standard deviation 0.0252.
(Type an integer or decimal rounded to four decimal places as needed.)
Draw a normal model with the area representing the P-value shaded for this hypothesis test. Choose the correct graph below, where the horizontal axis represents pfemale-pmale.
A normal curve is over a horizontal axis and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 0.0236. The area under the curve and to the right of the vertical line segment is shaded.

(e) Determine the P-value based on the model from part (d).
First find the test statistic for this hypothesis test.
0.94 (Round to two decimal places as needed.)
Determine the P-value for this hypothesis test.
0.174 (Round to three decimal places as needed.)

(f) Interpret the P-value.
If the population proportions are equal, one would expect a sample difference proportion greater than or equal to 0.0252 in about 174 out of 1000 repetitions of this experiment.
(Round to the nearest integer as needed.)

(g) Based on the P-value, what does the sample evidence suggest? That is, what is the conclusion of the hypothesis test? Assume an α=0.05 level of significance.
Do not reject H0. There is not sufficient evidence at the α=0.05 level of significance to suggest a higher proportion of females are annoyed by the behavior in question.

Added by Cesar H.

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