MATH 281 Introductory Statistics (Has Homework: U2 HW 8: Section 12.2 (Hypothesi

Question

MATH 281 Introductory Statistics (Has Homework: U2 HW 8: Section 12.2 (Hypothesis Test f Score1 pt 5 of 8 (1 complete) 12.2.81-P The number of successes and the sample size for a simple random sample from a population are given below xz9, n = 36, Ho : p#0.2. Ha: p#02, = 0.01 a. Determine the sample proportion b. Decide whether using the one-proportion z test is appropriate. c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test Click here to view page 1 of areas under the standard nomal curve for negative values of 2 Clck here to view page 1 of areas under the standard normal cunve for positive yalues of z a. The sample proportion is Type an integer or a decimat Do not round)

Explanation / Answer

Solution:

We are given x=9, n = 36

H0: p = 0.2 Vs Ha: p 0.2, = 0.01

Part a

Sample proportion = x/n = 9/36 = 0.25

Part b

One proportion z test is appropriate because we are dealing with single population proportion.

Part c

Test statistic = Z = (P – p)/sqrt(p*(1 – P)/n)

Z = (0.25 – 0.20)/sqrt(0.20*0.80/36)

Z = 0.05/ sqrt(0.20*0.80/36)

Z = 0.75

Critical value = 2.5758

P-value = 0.4533

= 0.01

P-value > = 0.01

So, we do not reject the null hypothesis at 1% level of significance.

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