Answer:
Step-by-step explanation:
Notation
is the sample mean
indicates the population mean (the variable of interest)
s signifies the sample standard deviation
n denotes the sample size
Solution to the problem
The mean's confidence interval is derived from the following formula:
(1)
In this instance, the 9% confidence interval corresponds to:
We can determine the mean using the following:
Additionally, the margin of error can be calculated as:
The margin of error for this situation is expressed as:
Next, we find the standard error:
The critical value for a 95% confidence interval using a normal standard distribution is roughly 1.96, and substituting gives us:
For the 98% confidence interval, the significance corresponds to 
and 
with a critical value of 2.326, yielding a confidence interval of:
The domain is defined as the complete set of values of variable x for which the function is valid. In this case, the x-axis illustrates time in seconds. Therefore, we must determine all possible time values over which distance can be covered or the function is defined. It’s noted that the sprinter completed the race in 11 seconds, and the start time is 0 seconds. Hence, the value of t ranges from 0 to 11. Therefore, the domain encompasses all real numbers from 0 to 11.
18.95(0.3 + 0.1) is the formula to use.
Response:
Maureen's null hypothesis is, H₀: p₁ ≥ p₂.
Detailed explanation:
Maureen McIlvoy, as the owner and CEO of a mail-order business specializing in windsurfing gear, is scrutinizing the order fulfillment processes in her warehouses. Her objective is to achieve a 100% shipment rate of orders within 24 hours. Upon examining her warehouse operations, she discovers that both the East coast and West coast warehouses have not met this goal, although the East Coast warehouse has consistently outperformed its counterpart.
To verify this finding, Maureen’s team randomly sampled 200 orders from the West Coast warehouse (population 1) and 400 from the East Coast warehouse (population 2).
Of the sampled 200 orders from the West Coast warehouse, 190 were delivered within the specified time. In contrast, 372 out of 400 orders from the East Coast warehouse were processed within 24 hours.
The hypotheses can be formulated as followed:
H₀: The proportion of timely shipments from the East Coast does not exceed that from the West Coast warehouse, thus, p₁ ≥ p₂.
Hₐ: The proportion of timely shipments from the East Coast warehouse is indeed greater than that from the West Coast warehouse, stated as p₁ < p₂.
Thus, Maureen's null hypothesis becomes, H₀: p₁ ≥ p₂.
