Susan and terry run a day care center Since they use susans house it was agreed that her share is twice as Terrys if they earn 2
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Answer:
a) Null and alternative hypothesis
b) Test statistic t=-1.565
P-value = 0.0612
NOTE: the sample size is n=65.
c) Do not reject H0. We cannot conclude that the 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.
d) Null and alternative hypothesis
Test statistic t=-1.565
Critical value tc=-1.669
t>tc --> Do not reject H0
Do not reject H0. We cannot conclude that the 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:
This is a hypothesis test for the population mean.
The claim is 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.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=65.
The sample mean is M=30.15.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim 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.
<u>Critical value approach</u>
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At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.
As the test statistic is greater than the critical value, it falls in the acceptance region.
The null hypothesis failed to be rejected.
Answer:
- Part A: The price of fuel A is decreasing by 12% per month.
- Part B: Fuel A recorded a greater percentage change in price over the previous month.
Explanation:
<u>Part A:</u>
The function calculates the price of fuel A each month by multiplying the price of the month before by 0.88.
Month price, f(x)
1 2.27 (0.88) = 1.9976 ≈ 2.00
2 2.27(0.88)² = 1.59808 ≈ 1.60
3 2.27(0.88)³ = 1.46063 ≈ 1.46
Then, the price of fuel A is decreasing.
The percentage per month is (1 - 0.88) × 100 = 12%, i.e. the price decreasing by 12% per month.
<u>Part B.</u>
<u>Table:</u>
m price, g(m)
1 3.44
2 3.30
3 3.17
4 3.04
To find if the function decreases with a constant ration divide each pair con consecutive prices:
- ratio = 3.30 / 3. 44 = 0.959 ≈ 0.96
- ratio = 3.17 / 3.30 = 0.960 ≈ 0.96
- ratio = 3.04 / 3.17 = 0.959 ≈ 0.96
Thus, the price of fuel B is decreasing by (1 - 0.96) × 100 =4%.
Hence, the fuel A recorded a greater percentage change in price over the previous month.