According to Vivino, a retailer specializing in high quality wines, the mean price for a bottle of red wine that scores four stars or higher on the Vivino Rating System is $32.88. A New England based lifestyle magazine wants to determine if these red wines areless expensivein Providence, a city in New England. They collected prices for 56 randomly selected red wines that scored four stars or higher from wine stores throughout Providence and found the mean and standard deviation for this sample to be $31.31 and $5.26, respectively.

(a) State the hypotheses to test the above claim:

H₀:

---

p

p

y

---

<

>

=

---

32.88

31.31

H_a:

---

p

p

y

---

<

>

=

---

32.88

31.31

(b) The test statistic for this data is -2.2335. Find and interpret the correspondingp-value. Use= 0.05.

(i) Thep-value =(4 decimals)

(ii) Interpret thisp-value as a probability, with reference to the 5% significance level: The abovep-value indicates that the probability of obtaining our sample statistic or one more extreme would be

---

unlikely

likely

to occur, under the assumption that the red wines of four stars or higher would cost

---

less

the same

in Providence.