Suppose that Mairin has knit a collection of wool-blend infinity scarves that sh
ID: 2949597 • Letter: S
Question
Suppose that Mairin has knit a collection of wool-blend infinity scarves that she wants to sell in her Etsy shop for $27.50 each. However, she is worried that if the average price of comparable scarves is less than $27.50, hers would be less likely to sell. Mairin selected a random sample of 8 similar hand-knit, wool-blend infinity scarves, and their prices are as follows $29.75, $24.00, $26.00, $27.99, $23.00, $22.50, $31.99, $25.00 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 $27.50. Assume that the prices of all comparable scarves are normally distributed Have the requirements for a one-sample t-test been met? If they have not been met, leave the remaining questions blank. ONo, Mairin selected a normally distributed random sample, but she does not know the population standard deviation. O Yes, Mairin selected a random sample from a normally distributed population, and her sample contains no outliers ONo, Mairin selected a random sample from a normally distributed population, but her sample is too small O Yes, Mairin selected a random sample that is normally distributed and contains no outliers Choose the appropriate null and alternative hypotheses for this test. 0 ? ? $26.28 O$27.50 Ox $26.28 ? ? $27.50 Ou $26.28 0 ?Explanation / Answer
H0 : mu = 27.50
H1 : mu < 27.50
t value at 95% = 2.0686
CI = (x1 -x2) +/- t * sqrt(s1^2/n1 +s2^2/n2)
= ( 14704 - 15022) +/- 2.0686 *sqrt(6215^2/36 + 7864^2/24)
= (-4269.9039,3633.9039)
= ( -4270 , 3634)
Lower limit = -4270 Upper limit = 3634
SE = sqrt(s1^2/n1 +s2^2/n2)
= sqrt(40.3^2/14 + 25.9^2/14)
= 12.803
t value at 95% = 2.0686
m = t * SE
= 2.0686 * 12.803
= 26.5