Which inequality is true if p = 3.4 ?
1 answer:
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Answer: x" = 5.69
Step-by-step explanation:
The graphic solution is attached.
Verifying the solution:
Existence condition: x > 0
2x - 4 = √x + 5
√x =2x - 4 - 5
√x =2x - 9 (²)
x = (2x - 9)²
x = 4x² - 36x + 81
4x² - 36x - x + 81 = 0
4x² - 37x + 81 = 0
Δ = -37² - 4.4.81 = 1369 - 1296 = 73
x = 37 ±√73/8
x' = 3.55
x" = 5.69
checking:
2*3.55 - 4 = 3.1
√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution
2*5.69 - 4 = 7.39
√5.69 + 5 = 7.39 ∴ it's the only solution
Answer:
50.34% probability that the sample mean would differ from the true mean by less than 1.1 months
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months
This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So
X = 120.1
By the Central Limit Theorem
has a pvalue of 0.7517
X = 117.9
has a pvalue of 0.2483
0.7517 - 0.2483 = 0.5034
50.34% probability that the sample mean would differ from the true mean by less than 1.1 months
Answer:
a) The hypothesis that the mean annual income is the same could not be rejected. There is no enough evidence to claim they are different.
b) The critical values for this two-sided test are t=±1.711.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>(a) Identify the claim and state H0 and Ha. </em>
<em> Which is the correct claim below?</em>
<em>(b) Find the critical value(s) and identify the rejection region(s). </em>
<em> Enter the critical value(s) below.</em>
We have an hypothesis test on the difference of two means.
The null and alternative hypothesis are:
The claim of the alternative hypothesis is that the mean annual income is different in County A and County B.
The null hypothesis is that the mean annual income is equal in both counties.
The significance level is α=0.10.
The sample from County A has a mean of S40,400, a s.d. of $8,700 and a sample size of 18 residents.
The sample from County B has a mean of S39,200, a s.d. of $6,000 and a sample size of 8 residents.
The standard error of the difference of means is:
The degrees of freedom are:
Then, the test statistic is:
For a statistic t=0.407, and df=24, the P-value is P=0.69. As the P-value is bigger than the significance level, the null hypothesis failed to be rejected.
If we would use the critial value approach, we would have to calculate the critical values for t, for df=24, two sided test and α=0.10.
The critical values, looking in a table, are t=1.711.