Question

Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves 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 the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed.

Choose the appropriate null and alternative hypotheses for this test.

Calculate the ?t‑test statistic. Round your answer to three decimal places.

$28.00.

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

her null hypothesis. There is

Mairin should

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

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

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

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

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

No, Mairin selected a normally distributed random sample, but she 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 1

Solution:
Given:

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

Yes, Mairin selected a random sample from a normally distributed population, 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 = 1.084 fall and then find corresponding one tail area.

t = 1.084 fall in between 0.889 and 1.108 , corresponding one tail 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 level of significance, hence we fail to reject H0.

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