# 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.