Question

1. Human Body Temperature. A sample of 115 body temperatures with a mean of 98.20℉ and a standard deviation of 0.62℉. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 97.6℉, as is commonly believed. Is there sufficient evidence to conclude that the common belief wrong?

2. Smartphone Users. A Ring Central survey of 395 smartphone users showed that 158 of them said that their smartphone is the only thing they could not live without. Use a 0.01 significance level to test the claim that fewer than half of smartphone users identify the smartphone as the only thing they could not live without. Do these results apply to the general population?

Answer 1

Solution :

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 97. 6
Alternative Hypothesis, Ha: μ ≠ 97.6

Rejection Region
This is two tailed test, for α = 0.05 and df = 114
Critical value of t are -1.981 and 1.981.
Hence reject H0 if t < -1.981 or t > 1.981

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (98.2 - 97.6)/(0.62/sqrt(115))
t = 10.378

reject the null hypothesis
There is sufficient evidence that the common belief is wrong.

2)

null Hypothesis:              Ho:   p=	0.500
alternate Hypothesis:    Ha: p <	0.500
for 0.01 level and left tailed test , critical z=	-2.33	(from excel:normsinv(0.01)
Decision rule :   reject Ho if test statistic z < 2.33

sample success x   =	158
sample size          n    =	395
std error σp =√(p*(1-p)/n) =	0.0246
sample prop p̂ = x/n=158/395=	0.4000
z =(p̂-p)/σp=(0.4-0.5)/0.0246=	-4.065

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that fewer than half of smartphone users identify the smartphone as the only thing they could not live without

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