There are five different colored cards in a hat (red, blue, green, yellow, and black). A card is randomly drawn and not replaced
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Answer:
Test statistic = 1.3471
P-value = 0.1993
Accept the null hypothesis.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 4
Sample mean, = 4.8
Sample size, n = 15
Alpha, α = 0.05
Sample standard deviation, s = 2.3
First, we design the null and the alternate hypothesis
We use two-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
Now, we calculate the p-value.
P-value = 0.1993
Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept it.
Consider such events:
A - slip with number 3 is chosen;
B - the sum of numbers is 4.
You have to count
Use formula for conditional probability:
1. The event consists in selecting two slips, first is 3 and second should be 1, because the sum is 4. The number of favorable outcomes is exactly 1 and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event
is
2. The event consists in selecting two slips with the sum 4. The number of favorable outcomes is exactly 2 (1st slip 3 and 2nd slip 1 or 1st slip 1 and 2nd slip 3) and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event
is
3. Then
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