n a soup factory, we take a random sample of8 cans of tomato soup, and measure t
ID: 3365706 • Letter: N
Question
n a soup factory, we take a random sample of8 cans of tomato soup, and measure their sodium content (in mg). The following are our observations 510 520 515 516 517 519 522 510 (a) (1 mark) Give the command and output to create a 96% confidence interval for the mean sodium content (b) (1 mark) Using your confidence interval, decide if 515 is a reasonable estimate for . (c) (1 mark) Give the command and output to test the alternative hypothesis that the mean sodium content is less than 520 mg (d) (1 mark) What is the observed value of the test statistic? (e) (1 mark) What is the p-value for our test? (f) (1 mark) If we were testing at a significance level of a = 0.01, what would the conclusion be?Explanation / Answer
a]
> t.test(x,mu=520,conf.level=0.96)
One Sample t-test
data: x
t = -1.0512, df = 7, p-value = 0.3281
alternative hypothesis: true mean is not equal to 520
96 percent confidence interval:
312.1137 , 605.3863
b] 515 is a reasonable estimate because 515 belong to the 96% confidence interval.
c]
> x=c(510,520,515,516,517,519,522,51)
> mu=520
> t.test(x,mu=520,alt="less",conf.level=0.96)
One Sample t-test
data: x
t = -1.0512, df = 7, p-value = 0.164
alternative hypothesis: true mean is less than 520
96 percent confidence interval:
-Inf 577.959
sample estimates:
mean of x
458.75
d] observed value =t test= -1.0512
e] pvalue = 0.164
f]
> t.test(x,mu=520,conf.level=0.99,alternative="less")
One Sample t-test
data: x
t = -1.0512, df = 7, p-value = 0.164
alternative hypothesis: true mean is less than 520
99 percent confidence interval:
-Inf 633.423
sample estimates:
mean of x
458.75
Only the confidence interval will change.
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