single proportionsingle mean (a) What is the level of significance? State the nu

Question

single proportionsingle mean     

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: ? = 0.35; H1:  ? < 0.35H0: p = 0.35; H1:  p ? 0.35     H0: p = 0.35; H1:  p < 0.35H0: ? = 0.35; H1: ? > 0.35H0: p = 0.35; H1: p > 0.35H0: ? = 0.35; H1:  ? ? 0.35

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since np < 5 and nq < 5.The Student's t, since np < 5 and nq < 5.     The standard normal, since np > 5 and nq > 5.The Student's t, since np > 5 and nq > 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.There is insufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.

at the professor has underestimated the number o students with part-time o full-time obs A andom sam le of 7 student Professor Jennings claims that only 35% o the students at Flora College work hile attending school. Dean Renata thinks have jobs. Do the data indicate that more than 35% of the students have jobs? Use e 5% level of significance. that 37 1:30:58 What are we testing in this problem? o single proportion single mean (a) What is the level of significance? 0.05 State the nul and alternate hypotheses. Ho 0.350.35 HD: ? . 0.35; HI: ? z 0.35 MO: ?-0.35; H1 : ? 0.35 Mo: 0.35: 10.35 (b) What sampling distribution will you use? What assumptions are you making? The standard normal, since np 5 and no > 5 The Student's t, since npS and nq5 What is the value of the sample test statistic? (Round your answer to two decimal places (c) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the aree corresponding to the P-value.

Explanation / Answer

State the null and alternate hypotheses

e that more than 35% of the stude

H0:p=0.35

H1:p>0.35

option E

(a) What is the level of significance?

alpha=0.05

What are we testing in this problem?

single proportion

n=77

p=37/77

q=40/77

np=37>5

nq=40>5

so np>5,nq>5

The standard normal, since np > 5 and nq > 5

What is the value of the sample test statistic?

z=p^-p/sqrt(p(1-p)/n

p^=37/77=0.480519

1-p^=1-0.480519=0.519481

z=0.480519-0.35/sqrt(0.35*(1-0.35)/77)

z=2.40

test statistic,z=2.40

(c) Find the P-value. (Round your answer to four decimal places.)

p =0.0082

solutiond:

p=0.0082

alpah=0.05

p<0.05

reject Null hypothesis.

Solutiond:

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs

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