Adam and his dad share the cost of the meal in the ratio of 2:3. Adam’s dad pays £52.20. What is the total cost of the meal
1 answer:
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A graph shows zeros to be ±3. Factoring those out leaves the quadratic
(x-2)² +1
which has complex roots 2±i.
The function has roots -3, 3, 2-i, 2+i.
A graph shows zeros to be ±3. Factoring those out leaves the quadratic
(x-2)² +1
which has complex roots 2±i.
The function has roots -3, 3, 2-i, 2+i.
Answer:
0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
Normal probability distribution.
Problems of normally distributed samples can be 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.
In this problem, we have that:
Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.
This probability is the pvalue of Z when . So
has a pvalue of 0.0062. So there is a 0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.
Answer:
So on this case for the significance level assumed we see that
so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.
So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.
Step-by-step explanation:
Let's suppose that we have the following linear model:
Where Y is the dependent variable and X the independent variable. represent the intercept and
the slope.
In order to estimate the coefficients we can use least squares procedure.
If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:
Null Hypothesis:
Alternative hypothesis:
Or in other words we want to check is our slope is significant (X have an effect in the Y variable )
In order to conduct this test we are assuming the following conditions:
a) We have linear relationship between Y and X
b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable
c) We assume that the Y values are independent and the distribution of Y is normal
The significance level assumed on this case is
The standard error for the slope is given by this formula:
Th degrees of freedom for a linear regression is given by since we need to estimate the value for the slope and the intercept.
In order to test the hypothesis the statistic is given by:
The p value on this case would be given by:
So on this case for the significance level assumed we see that
so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.
So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.