Saul has 130 baseball cards. How many baseball cards does he need to get so that he will have 200 baseball cards in all?
2 answers:
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Answer:
Part A
b. 14.6 ± 7.38
Part B
b. 3.43
Part C
a. P-value < 0.01
Part D
b. There is sufficient evidence to reject the null hypothesis
Step-by-step explanation:
Part A
The given data are;
The number of seedlings in the field = 20
The number of seedlings selected to receive herbicide A = 10
The number of seedlings selected to receive herbicide B = 10
The height in centimeters of seedlings treated with Herbicide A, = 94.5 cm
The standard deviation, s₁ = 10 cm
The height in centimeters of seedlings treated with Herbicide B, = 109.1 cm
The standard deviation, s₂ = 9 cm
The 90% confidence interval for μ₂ - μ₁, is given as follows;
The critical-t at 95% and n₁ + n₂ - 2 degrees of freedom is given as follows;
The degrees of freedom, df = n₁ + n₂ - 2 = 10 + 10 - 2 = 18
α = 100% - 90% = 10%
∴ For two tailed test, we have, α/2 = 10%/2 = 5% = 0.05
= 1.734
C.I. ≈ 14.6 ± 7.37714603353
The 90% C.I. ≈ 14.6 ± 7.38
b. 14.6 ± 7.38
Part B
With the hypotheses are given as follows;
H₀; μ₂ - μ₁ = 0
Hₐ; μ₂ - μ₁ ≠ 0
The two sample t-statistic is given as follows;
The two sample t-statistic ≈ 3.43
b. 3.43
Part C
From the t-table, the p-value, we have, the p-value < 0.01
a. P-value < 0.01
Part D
Given that a significance level of 0.05 level is used and the p-value of 0.01 is less than the significance level, there is enough statistical evidence to reject the null hypothesis
b. There is sufficient evidence to reject the null hypothesis.
Combination = doesn't matter what order
Permutation = order matters
There are <u>two</u> methods to work out combinations.
Method 1 List out possibilities
123 124 125 126 127 134 135 136 137 145 146 147 156 157 167
234 235 236 237 245 246 247 256 257 267
345 346 347 356 357 367
456 457 467
567
For a total of 35 combinations.
Method 2 Use a formula.
It's a rather complicated one, so only use it if you have a lot of possibilities.
(n is the number of choices, r is the amount you choose, and ! is a function that multiplies together all numbers down to 1)
Permutation = order matters
There are <u>two</u> methods to work out combinations.
Method 1 List out possibilities
123 124 125 126 127 134 135 136 137 145 146 147 156 157 167
234 235 236 237 245 246 247 256 257 267
345 346 347 356 357 367
456 457 467
567
For a total of 35 combinations.
Method 2 Use a formula.
It's a rather complicated one, so only use it if you have a lot of possibilities.
(n is the number of choices, r is the amount you choose, and ! is a function that multiplies together all numbers down to 1)