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.
Calculate the ?t‑test statistic. Round your answer to threedecimal places.
$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
Answer:
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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