Cynthia is mowing lawns for extra money. The amount of money she made after putting gas in the lawnmower is shown below.
2 answers:
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Answer:
209 points
Step-by-step explanation:
Mean points scored (μ) = 182 points
Standard deviation (σ) = 14 points
The z-score for any given game score 'X' is defined as:
At, the 97th percentile of a normal distribution, the z-score, according to a z-score table, is 1.881.
Therefore, the minimum score, X, needed for a bowler to receive a trophy is:
Since only whole point scores are possible, X=209 points.
Answer:
a) We can reject the null hypothesis and conclude that average battery time is shorter than 4 hours at a = 0.05
b) 95% confidence interval of the mean battery time is 230±11.55. That is between 218.45 min and 241.55 min.
c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, we can conclude that we fail to reject the null hypothesis, because confidence interval includes 240 min.
d) We made a correct decision at c, if study establishes that in fact, a population mean is 4 hours.
Step-by-step explanation:
a)
H0: µ=240
H1: µ<240
Test statistic can be found using the equation
where
- X = 230 min. (3 hours 50 minutes)
- M is the lasting time of laptop batteries claimed in null hypothesis (240 min.)
- s is the sample standard deviation (20 minutes)
- N is the sample size (16)
= -2
<em>One tailed</em> p-value of t=-2 for 15 <em>degrees of freedom</em> is ≈ 0.032
Since 0.032<0.05, the result is significant. We can reject the null hypothesis and conclude that average battery time is shorter than 4 hours at a = 0.05
b) 95% confidence interval of the mean battery time can be calculated using M±where
- M is the sample average lasting time (230 min)
- t is the<em> two tailed</em> statistic for 95% confidence level and 15 <em>degrees of freedom</em> (2.13)
- s is the sample standard deviation (20 min.)
- n is sample size (16)
230± that is 230±11.55
c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, from 95% confidence interval which is between 218.45 min and 241.55 min, we can conclude that we fail to reject the null hypothesis, because confidence interval includes 240 min.
d) We made a correct decision at c, if study establishes that in fact, a population mean is 4 hours.