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 528 males surveyed, 210 responded "yes": among the 512 females surveyed. 215 responded "yes." does the evidence suggest a higher proportion of females are annoyed by this behavior? complete parts (a) through (d) below.

a. determine the sample proportion for each sample. the proportions of the females and males who took the survey who are annoyed by the behavior in question are __ and 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.

a. the data come from a population that is normally distributed.
b. the sample size is less than 5% of the population size for each sample.
c. the sample size is more than 5% of the population size for each sample.
d. the samples are dependent.
e. the samples are independent.
f. n_1p_1^hat (1 - p_1^hat) greaterthanorequalto 10 and n_2p_2^hat (1- p_2^hat) greaterthanorequalto 10

c. what are the null and alternative hypotheses? let p_1 represent the population proportion of females who are annoyed by the behavior in question and p_2 represent the population proportion of males who are annoyed by the behavior in question. h_0: p_1 p_2 h_1: p_1 p_2

d. describe the sampling distribution of p^hat_female - p^hat_male draw a normal model with the area representing the p-value shaded for this hypothesis test. the sampling distribution is approximately normal with mean __ and standard deviation (type an integer or decimal rounded to four decimal places as needed.)