Answer:
a
The null hypothesis is
The alternative hypothesis is ![H_a : \mu < 32.48](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20%5Cmu%20%20%3C%20%2032.48)
b
![t = -1.504](https://tex.z-dn.net/?f=t%20%20%3D%20%20-1.504)
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 ![\mu = \$ 32.48](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20%5C%24%2032.48)
The sample size is n = 56
The sample mean is ![\= x = \$30.15](https://tex.z-dn.net/?f=%5C%3D%20%20x%20%20%3D%20%20%5C%2430.15)
The standard deviation is ![\sigma = \$12](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%20%5C%2412)
The null hypothesis is
The alternative hypothesis is ![H_a : \mu < 32.48](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20%5Cmu%20%20%3C%20%2032.48)
Generally the test statistic is mathematically represented as
![t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B%5C%3D%20x%20%20-%20%5Cmu%20%7D%7B%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
=> ![t = \frac{30.15 - 32.48 }{\frac{12 }{\sqrt{60} } }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B30.15%20%20-%2032.48%20%7D%7B%5Cfrac%7B12%20%7D%7B%5Csqrt%7B60%7D%20%7D%20%7D)
=> ![t = -1.504](https://tex.z-dn.net/?f=t%20%20%3D%20%20-1.504)
Generally the p-value is mathematically represented as
![p-value = P (t < -1.504 )](https://tex.z-dn.net/?f=p-value%20%20%3D%20%20P%20%28t%20%3C%20-1.504%20%29)
From the z-table
![P(t < -1.504) = 0.066291](https://tex.z-dn.net/?f=P%28t%20%3C%20%20-1.504%29%20%3D%20%20%200.066291)
So
![p-value = 0.066291](https://tex.z-dn.net/?f=p-value%20%20%3D%200.066291%20)
From the value we obtain we see that
![p -value > \alpha](https://tex.z-dn.net/?f=p%20-value%20%20%3E%20%20%5Calpha)
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
Answer:
Step-by-step explanation:
480 because you multipy 4 times 8 and than you mulpyy 48 times 10 and that is how i got the number 480.
The function of x is equal to 7 dollars times the number of hours the cashier works. This function would look something like this:
F(x) = 7x
Hope this helps! :)
Answer: 16/25
<h2>Solution with Steps</h2>
4/10 divided by 5/8 = ?
Dividing two fractions is the same as multiplying the first fraction by the reciprocal or inverse of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes -
4/10 x 8/5 = ?
For fraction multiplication, multiply the numerators and then multiply the denominators to get -
Numerators: 4 x 8 = 32
Denominators: 10 x 5 = 50
Fraction: 32/50
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 32 and 50. The GCF (Greatest Common Factor) would be 2.
Numerator: 32 / 2 = 16
Denominator: 50 / 2 = 25
Fraction: 16/25
<h2>Another Solution</h2>
4/10 divided by 5/8 = ?
Cross multiply -
Numerator x Denominator: 4 x 8 = 32
Denominator x Numerator: 10 x 5 = 50
Fraction: 32/50
Reduce by dividing both the numerator and denominator by the Greatest Common Factor, which is 2.
Numerator: 32 / 2 = 16
Denominator: 50 / 2 = 25
Fraction: 16/25