Mathematics, 10.01.2020 06:31 amanda2517

The director of student activities is concerned that she has not hired enough security for the sadie hawkins day dance, and wants to know approximately how many students will be attending. if more than 25% of the student body is planning on going to the dance, she will need to hire more security. she sends out a survey to 300 students, and out of the 285 who respond, 82 say they plan to attend.

on the basis of this survey, should the director of student activities hire more security? use appropriate statistical evidence to support your conclusion.

there were 15 people who didn't return their surveys. suppose they had.

is it possible that the student activities director's decision would have been different?

Answers: 3

Show answers

Answers

Answer from: diyah843

Assuming 0.05 significance level, there is no significant evidence, on the basis of this survey, that the Director of Student Activities has to hire more security.

If 15 people who didn't return their surveys had returned their surveys and all reported attending the dance, Student Activities Director's decision would have been different, because there would be significant evidence on the basis of this survey, that the Director of Student Activities has to hire more security.

Step-by-step explanation:

Lep p be the proportion of students who will attend the Sadie Hawkins Day dance.

Null and alternative hypotheses are:

$H_{0}:$ p=0.25 $H_{a}:$ p>0.25

Test statistic can be calculated using the equation:

z= $\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }$ where

p(s) is the sample proportion of students who will attend the Sadie Hawkins Day dance ( $\frac{82}{285}$ ≈0.288)p is the proportion assumed under null hypothesis. (0.25)N is the sample size (285)

Then z= $\frac{0.288-0.25}{\sqrt{\frac{0.25*0.75}{285} } }$ ≈ 1.48

Corresponding one tailed p-value for the test statistics is ≈ 0.069

Assuming a significance level 0.05, the result is not significant since 0.069>0.05.

Therefore there is not significant statistical evidence at 0.05 significance level that the director has to hire more security.

Suppose 15 people who didn't return their surveys had returned their surveys and all reported attending the dance.

Then above sample proportion of students who will attend the Sadie Hawkins Day dance changed as ( $\frac{97}{300}$ ≈0.323). Sample size would be 300.

If we recalculate the test statistic:

z= $\frac{0.323-0.25}{\sqrt{\frac{0.25*0.75}{300} } }$ ≈ 2.92

And p-value is ≈ 0.00175. This result is significant at 0.05 significance level,

Therefore in this case (if 15 people who didn't return their surveys had returned their surveys and all reported attending the dance) Student Activities Director's decision would have been different

Answer from: Quest

idk

step-by-step explanation:

Answer from: Quest

d. all of the above

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Find the length of the following tangent segments to the circles centered at o and o' whose radii are 5 and 3 respectively and the distance between o and o' is 12. what is the tangent segment of cd?

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

What are the related frequencies to the nearest hundredth of the columns of the two way table? group 1: a-102 b-34group 2: a-18 b-14edited: i don’t have all day to be waiting for an answer. i figured it out.

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

Amanager recorded the number of bicycles sold by his company each quarter. his projected sales after t years is given by the expression below. which of the following statements best describes the expression? a. the initial sales of 575 bicycles increases at the rate of 4% over 4 quarters. b. the initial sales of 575 bicycles increases at the rate of 18% over 4 years. c. the initial sales of 575 bicycles increases at the rate of 4% over t quarters. d. the initial sales of 575 bicycles increases at the rate of 18% over t years.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Ann and betty together have $60 ann has $9 more than twice betty’s amount how much money dose each have

Answers: 1

Answer

You know the right answer?

The director of student activities is concerned that she has not hired enough security for the sadie...

Questions

Mathematics, 20.09.2019 17:10

Aresearcher wants to find out the average amount of money that united states (us) adults spent on gifts during november and december of the previous y...

Mathematics, 20.09.2019 17:10