A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have accepta
1 answer:
Answer:
0.392, independent
Step-by-step explanation:
Given that a certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Suppose that 90% of all batteries from a certain supplier have acceptable voltages.
For determining the probability we must assume that the batteries' voltage levels are independent
Let X be the no of batteries acceptable in the sample of 20 selected.
Then X is binomial because only two outcomes, and independence is assumed
Required proability = the probability that at least nineteen will work
=
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Answer:
Null hypothesis:
Alternative hypothesis:
Comparing the p value with the significance level assumed we see that
so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the number of people indicating that their financial security was more than fair for the recent year
represent the number of people indicating that their financial security was more than fair for the year before
sample 1 selected
sample 2 selected
represent the proportion estimated of indicating that their financial security was more than fair this year
represent the proportion estimated of indicating that their financial security was more than fair the year before
represent the pooled estimate of p
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level assumed we see that
so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.
From the given data we shall obtain the following boxplot, which we can generate the information given:
<span>5.5, 5.7, 5.8, 6.0, 6.1, 6.1, 6.3, 6.4, 6.5, 6.6, 6.7, 6.7, 6.7, 6.9, 7.0, 7.0, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.7, 7.7, 7.8, 8.0, 8.1, 8.1, 8.3, 8.7
1st Qu=6.425
3rd Qu=7.650
</span>
<span>5.5, 5.7, 5.8, 6.0, 6.1, 6.1, 6.3, 6.4, 6.5, 6.6, 6.7, 6.7, 6.7, 6.9, 7.0, 7.0, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.7, 7.7, 7.8, 8.0, 8.1, 8.1, 8.3, 8.7
1st Qu=6.425
3rd Qu=7.650
</span>