Answer:
Step-by-step explanation:
For the null hypothesis,
H0: p = 88
For the alternative hypothesis,
Ha: p < 88
Considering the population proportion, probability of success, p = 0.88
q = probability of failure = 1 - p
q = 1 - 0.88 = 0.12
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 21
n = number of samples = 32
P = 21/32 = 0.66
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.66 - 0.88)/√(0.88 × 0.12)/32 = - 3.83
The corresponding p value would be determined by looking at the normal distribution table for the area below the z score. Therefore,
P value = 0.00006
Answer: A. 664
Step-by-step explanation:
Given : A marketing firm is asked to estimate the percent of existing customers who would purchase a "digital upgrade" to their basic cable TV service.
But there is no information regarding the population proportion is mentioned.
Formula to find the samples size , if the prior estimate to the population proportion is unknown :
, where E = Margin of error.
z* = Two -tailed critical z-value
We know that critical value for 99% confidence interval = [By z-table]
Margin of error = 0.05
Then, the minimum sample size would become :
Simplify,
Thus, the required sample size= 664
Hence, the correct answer is A. 664.
The expression (5³)⁹÷5¹² is simplified to 5^15
<h3>What are index forms?</h3>
Index forms are defined as the exponent or power of a number or variables.
It is also seen as a mathematical method of writing numbers that are too large or too small in simpler forms.
The laws of exponents are;
- Add the powers when they are being multiplied the bases are the same
- Subtract the exponents when they are divided and have the same base.
- Multiply the exponents when the bases are the same
Given the expression;
(5³)⁹÷5¹²
This is represented as;
(5³)⁹/5¹²
expand the bracket
5^27/5^12
Take the inverse exponent of the denominator
5^27-12
5^15
Thus, the simplified form is 5^15
Learn more about index forms here:
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