# Suppose that Mairin has knit a

Suppose that Mairin has knit a collection of wool‑blend infinityscarves that she wants to sell in her Etsy shop for \$28.00 each.However, she is worried that if the average price of comparablescarves is less than \$28.00, hers would be less likely to sell.

Mairin selected a random sample of 9 similar hand‑knit,wool‑blend infinity scarves, and their prices are as follows.

\$21.75,\$24.00,\$27.25,\$29.95,\$23.00,\$26.00,\$27.80,\$33.50,\$27.00\$21.75,\$24.00,\$27.25,\$29.95,\$23.00,\$26.00,\$27.80,\$33.50,\$27.00

Use a left‑tailed one‑sample ?t‑test to determine whether theaverage price of hand‑knit, wool‑blend infinity scarves sold onEtsy is less than \$28.00. Assume that the prices of all comparablescarves are normally distributed.

Choose the appropriate null and alternative hypotheses for thistest.

\$28.00.

Complete the conclusion of this test. Use a significance levelof ?=0.10α=0.10.

her null hypothesis. There is

Mairin should

evidence that the mean price of hand‑knit, wool‑blend infinityscarves is

Have the requirements for a one‑sample ?t‑test been met? If theyhave not been met, leave the remaining questions blank.

Yes, Mairin selected a random sample that is normallydistributed and contains no outliers.

Yes, Mairin selected a random sample from a normally distributedpopulation, and her sample contains no outliers.

No, Mairin selected a random sample from a normally distributedpopulation, but her sample is too small.

No, Mairin selected a normally distributed random sample, butshe does not know the population standard deviation.

?0:H0:

?⎯⎯⎯=\$28.00x¯=\$28.00

?=\$28.00μ=\$28.00

?⎯⎯⎯=\$26.69x¯=\$26.69

?=\$26.69μ=\$26.69

?1:H1:

?⎯⎯⎯=\$26.69x¯=\$26.69

?<\$28.00μ<\$28.00

?<\$26.69μ<\$26.69

?⎯⎯⎯<\$28.00x¯<\$28.00

?=t=

Use a ?t‑distribution table to find a range of possible?p‑values for this test.

0.15<?<0.200.15<p<0.20

0.20<?<0.250.20<p<0.25

0.05<?<0.100.05<p<0.10

0.10<?<0.15

Solution:Given:

Have the requirements for a one‑sample ?t‑test been met?

Yes, Mairin selected a random sample from a normally distributedpopulation, and her sample contains no outliers.

Step 1) State H0 and H1:

Step 2) Calculate t test statistic:

where

Thus we need to make following table:

 x x^2 21.75 473.0625 24.00 576 27.25 742.5625 29.95 897.0025 23.00 529 26.00 676 27.80 772.84 33.50 1122.25 27.00 729

Thus

Thus t test statistic

Step 3) Find p-value range:

df = n -1 = 9 – 1 = 8

Look in df = 8 row in t table for interval in which t = 1.084fall and then find corresponding one tail area.

t = 1.084 fall in between 0.889 and 1.108 , corresponding onetail area in between 0.15 to 0.20

Thus p-value range is: ( 0.15 < p < 0.20 )

Step 4) Conclusion:Since p-value is in between 0.15 to 0.20 , which is > 0.10 levelof significance, hence we fail to reject H0.

There is not sufficient evidence that the mean price ofhand‑knit, wool‑blend infinity scarves is less than \$28.00.

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