Answer:
a
The null hypothesis is [tex]H_o : \mu = 32.48[/tex]
The alternative hypothesis is [tex]H_a : \mu < 32.48[/tex]
b
[tex]t = -1.504[/tex]
c
There is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48
Step-by-step explanation:
From the question we are told that
The mean price of is [tex]\mu = \$ 32.48[/tex]
The sample size is n = 56
The sample mean is [tex]\= x = \$30.15[/tex]
The standard deviation is [tex]\sigma = \$12[/tex]
The null hypothesis is [tex]H_o : \mu = 32.48[/tex]
The alternative hypothesis is [tex]H_a : \mu < 32.48[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{30.15 - 32.48 }{\frac{12 }{\sqrt{60} } }[/tex]
=> [tex]t = -1.504[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P (t < -1.504 )[/tex]
From the z-table
[tex]P(t < -1.504) = 0.066291[/tex]
So
[tex]p-value = 0.066291 [/tex]
From the value we obtain we see that
[tex]p -value > \alpha[/tex]
Then we fail to reject the null hypothesis
Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48
