8/3/2019 Solution One Sample Sign Test

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Solution:

1. = 0.05, n = 35, plus sign = 9, minus sign = 26

Step 1:

H0 = M = 150

H1 = M 150

Step 2:

Since n 12, we use z-test,

z =

where, x = smaller number +/- sign

n = sample size

z =

z = -2. 7045

Step 3:

Since = 0.05, so the critical value is 1.96.

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Step 4:

Since -2.7045 are greater than -1.96, so we reject H0

Step 5:

There is enough evidence to reject the claim that the median = 150

Using P-Value Method:

Step 1:

H0 = M = 150 (claim)

H1 = M 150

Step 2:

Since n 12, we use z-test,

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z =

where, x = smaller number +/- sign

n = sample size

z =

z = -2. 7045

Step 3:

P(Z > -2.70449)

Using calculator we get, P-value : 0.0034205

Since it is two tailed case, so P-value is 2(0.0034205) = 6.841 x 10-3

Step 4:

Since 0.0034205< 0.05, so we reject H0

Step 5:

There is enough evidence to reject the claim that the median = 150

8/3/2019 Solution One Sample Sign Test

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2. Step 1: State the hypotheses and identify the claim.

H0:M 8 (claim) H1: M < 8

Step 2 : Find the critical value.

Since =0.05, n =50 and this is a left-tailed test, the critical value is

-1.96,obtained from the table of standard normal distribution, Table A.2.

Step 3: Compute the test statistic

z= =-0.99

step 4 : Make the decision

Since the test statistic of -0.99 is greater than -1.96, do not reject the null hypothesis.

Step 5: Conclusion

There is not enough evidence to reject the claim that the median lifetime of the washers is

at least 8 years.

8/3/2019 Solution One Sample Sign Test

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Using P-value method:

State the hypotheses and identify the claim.

H0:M 8 (claim) H1: M < 8

Compute the test statistic

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z =

= -0.98995

Using calculator,

P-value = P(Z< - 0.98995)

= 0.1611

Since 0.1611> 0.05,

Do not reject H0.

Not enough evidence to reject the claim.

8/3/2019 Solution One Sample Sign Test

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3. Step 1:

H0 = M 97.5

H1 = M < 97.5 (claim)

Step 2:

k = 2, n = 11

Using table A.1,

P(k 2 | 11) = 1.7651

Step 3:

Since 1.7651 > 0.05,

Do not reject H0.

Step 4:

8/3/2019 Solution One Sample Sign Test

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Not enough evidence to support the claim.

4. Step 1:

H0 = M 8.41

H1 = M > 8.41 (claim)

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Step 2:

Since n 12, we use z-test,

n = 15, k = 3

z =

z = -2. 06559

Step 3:

P(Z > -2.06559)

Using calculator we get, P-value : 0.019434

Step 4:

Since 0.019434 < 0.05, so we reject H0

Step 5:

There is enough evidence to support the claim that the median = 8.41