A bacteria culture is started with 200 bacteria. After 3 hours, the population of bacteria grows to 800 bacteria. If the populat
1 answer:
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Answer:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that have traded in their old car is lower than 0.48 or 48%.
Step-by-step explanation:
Data given and notation
n=115 represent the random sample taken
X=46 represent the number of people that have traded in their old car.
estimated proportion of people that have traded in their old car
is the value that we want to test
represent the significance level
Confidence=90% or 0.9
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion is less than 0.48.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that have traded in their old car is lower than 0.48 or 48%.
Answer:
Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.
Step-by-step explanation:
We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.
A random sample of 39 steel bolts is selected.
Let = <u><em>sample mean diameter</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean diameter = 141 millimetres
= standard deviation = 7 millimetres
n = sample of steel bolts = 39
Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P( > 141.4 millimetres)
P( > 141.4) = P(
>
) = P(Z > 0.36) = 1 - P(Z
0.36)
= 1 - 0.6406 = <u>0.3594</u>
The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.