Which group shows 0.25 of the faces smiling?
1 answer:
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Answer:
Ron's ERA has a z-score of -2.03.
Karla's ERA has a z-score of -1.86.
Due to the lower z-score, Ron had a better yean than Karla relative to their peers.
Step-by-step explanation:
Z-score:
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 question:
Since the lower the ERA, the better the pitcher, whoever's ERA has the lower z-score had the better year relative to their peers.
Ron
ERA of 3.06, so
For the males, the mean ERA was 5.086 and the standard deviation was 0.998. This means that
So
Ron's ERA has a z-score of -2.03.
Karla
ERA of 3.28, so
For the females, the mean ERA was 4.316 and the standard deviation was 0.558. This means that
So
Karla's ERA has a z-score of -1.86.
Which player had the better year relative to their peers, Ron or Karla?
Due to the lower z-score, Ron had a better yean than Karla relative to their peers.
We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.
Given,
The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.
In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.
To report the large-sample z statistic and its p-value,
Null hypothesis,
H₀ : p = 0.79
Alternative hypothesis,
Ha : p < 0.79
Level of significance, α = 0.01
Under H₀
Test statistic,
Z₀ = -7.948
The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by
P-value = P(z <-7.945)
= 0.000 (from z-table)
Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.
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