Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. Upper H 0 : p equals 0.84 versus Upper H 1 : p not equals 0.84 n equals 500 comma x equals 410 comma alpha equals 0.05 n=500, x=410, α=0.05 Is np 0 left parenthesis 1 minus p 0 right parenthesis greater than or equals 10np01−p0≥10​? Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. ​Yes, because np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0equals= nothing. B.​No, because np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0equals= nothing. Now find ModifyingAbove p with caretp. ModifyingAbove p with caretpequals= nothing ​(Type an integer or a decimal. Do not​ round.) Find the test statistic z 0z0. z 0z0equals= nothing ​(Round to two decimal places as​needed.) Find the​ P-value. ​P-valueequals= nothing ​(Round to three decimal places as​ needed.) State the conclusion of the hypothesis test. ▼ Reject the null hypothesis, Do not reject the null hypothesis, because the​ P-value is ▼ less greater than alphaα.

Question #2: In a clinical​ trial, 17 out of 833 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that 1.5% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 1.5% of this​ drug's users experience flulike symptoms as a side effect at the alpha equals 0.05 level of​ significance?

Because np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0equals=nothing

▼

greater than>

less than<

not equals≠

equals=

​10, the sample size is

▼

greater thangreater than

less thanless than

​5% of the population​ size, and the sample

▼

cannot be reasonably assumed to be random,

is given to be random,

can be reasonably assumed to be random,

is given to not be random,

the requirements for testing the hypothesis

2. What are the null and alternative hypothesis?

Ho _ _ _ versus H1_ _ _

3. Find the test statistic

Z0=

Find the p-value

P value equals:

4. Choose the correct choice below.

A. Since p value <a do not reject the null hypothesis and conlude that there is sufficient evidence that is more than

B. Since p value > a reject the null hypothesis and conclude that there is not suffiencent

C. Since p value <a reject the null hypothesis and conclude that there is sufficient evidence.

D. Since P value >a do not reject the null hypothesis and conclude that there is not sufficient evidence

And

Question #3: Twenty years​ ago, 49​% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 242 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did 20 years ago. Use a=0.05 as level of signfcance.

1. Because

np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0equals=nothing

▼

greater than>

not equals≠

equals=

less than<

​10,

the sample size is

▼

greater than less than ​5% of the population​ size, and the sample

▼is given to not be random, cannot be reasonably assumed to be random, is given to be random, can be reasonably assumed to be random, the requirements for testing the hypothesis are or are not satisfied.

What are the null and alternative​ hypotheses?

Upper H 0​:▼mupp

sigmaσ

▼

less than<

not equals≠

equals=

greater than>

nothing versus

Upper H 1H1​:

▼

muμ

sigmaσ

pp

▼

greater than>

equals=

not equals≠

less than<

nothing

​(Type integers or decimals. Do not​ round.)

Determine the test​ statistic,

z 0z0.

z 0=

​(Round to two decimal places as​ needed.)

Determine the critical​ value(s). Select the correct choice below and fill in the answer box to complete your choice.

​(Round to two decimal places as​ needed.)

A.

z Subscript alphazαequals=nothing

B.

plus or minus±z Subscript alpha divided by 2zα/2equals=plus or minus±nothing

Choose the correct conclusion below.

A.

RejectReject

the null hypothesis. There

is insufficientis insufficient

evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago.

B.

RejectReject

the null hypothesis. There

is sufficientis sufficient

evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago.

C.

Do not rejectDo not reject

the null hypothesis. There

is insufficientis insufficient

evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago.

D.

Do not rejectDo not reject

the null hypothesis. There

is sufficientis sufficient

evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from many years ago

And

Question #4: Two professors at a local college developed a new teaching curriculum designed to increase​ students' grades in math classes. In a typical developmental math​ course,

53% of the students complete the course with a letter grade of​ A, B, or C. In the experimental​ course, of the 16 students​ enrolled, 11 completed the course with a letter grade of​ A, B, or C. Is the experimental course effective at thealpha equals 0.025 level of​ significance? Complete parts ​D through​ (g).

​(d) Determine the​ P-value using the binomial probability distribution. State your conclusion to the hypothesis test.

First determine the​ P-value.

​P-valueequals=nothing

A.

YesYes​,

do not rejectdo not reject

the null hypothesis because the​ P-value is

greatergreater

than

alphaα.

There

is sufficientis sufficient

evidence to conclude that the experimental course is effective.

B.

NoNo​,

do not rejectdo not reject

the null hypothesis because the​ P-value is

greatergreater

than

alphaα.

There

is insufficientis insufficient

evidence to conclude that the experimental course is effective.

C.

NoNo​,

rejectreject

the null hypothesis because the​ P-value is

lessless

than

alphaα.

There

is insufficientis insufficient

evidence to conclude that the experimental course is effective.

D.

YesYes​,

rejectreject

the null hypothesis because the​ P-value is

lessless

than

alphaα.

There

is sufficientis sufficient

evidence to conclude that the experimental course is effective.​(e) Suppose the course is taught with

5757

students and

3636

complete the course with a letter grade of​ A, B, or C. Verify whether the normal model may now be used to estimate the​P-value.Because np 0 left parenthesis 1 minus p 0 right parenthesisnp01−p0equals=14.214.2

greater than>

greater than>

equals=

less than<

not equals≠

​10, the sample size is

less than

greater than

less than

​5% of the population​ size, and the sample

can be reasonably assumed to be random,

is given to be random,

cannot be reasonably assumed to be random,

is given to not be random,

can be reasonably assumed to be random,

the normal model

may

may not

may

be used to approximate the​ P-value.

​(Round to one decimal place as​ needed.)

​(f) Use the normal model to obtain and interpret the​ P-value. State your conclusion to the hypothesis test.

First find the test​ statistic,

z 0z0.

z 0z0equals=2.62.6

​(Round to two decimal places as​ needed.)

Now determine the​ P-value.

​P-valueequals=. 005.005

​(Round to three decimal places as​ needed.)

Is there sufficient evidence to support the research that the experimental course is​ effective?

A.

NoN

do not reject

the null hypothesis because the​ P-value is

greatergreater

than

alphaα.

There is

insufficientinsufficient

evidence to conclude that the experimental course is effective.

B.

NoNo​,

do not rejectdo not reject

the null hypothesis because the​ P-value is

lessless

than

alphaα.

There is

insufficientinsufficient

evidence to conclude that the experimental course is effective.

C.

YesYes​,

rejectreject

the null hypothesis because the​ P-value is

lessless

than

alphaα.

There is

sufficientsufficient

evidence to conclude that the experimental course is effective.

D.

YesYes​,

rejectreject

the null hypothesis because the​ P-value is

greatergreater

than

alphaα.

There is

sufficientsufficient

evidence to conclude that the experimental course is effective.

​(g) Explain the role that sample size plays in the ability to reject statements in the null hypothesis.

When there are small sample​ sizes, the evidence against the statement in the null hypothesis must be

substantial.

insignificant.

substantial.

One should be wary of studies that

reject

do not reject

reject

the null hypothesis when the test was conducted with a small sample size.

Answer 1

according to HomeworkLib rules I have solved first question