Respuesta :
Answer:
We conclude that the mean body temperature of all healthy adults is actually less than 98.6℉.
Step-by-step explanation:
We are given that researchers at the University of Maryland recorded body temperatures from a random sample of 93 healthy adults.
They obtained a sample mean of 98.42℉ and a standard deviation of 0.65℉.
Let [tex]\mu[/tex] = mean body temperature of all healthy adults.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 98.6℉ {means that the mean body temperature of all healthy adults is actually greater than or equal to 98.6℉}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 98.6℉ {means that the mean body temperature of all healthy adults is actually less than 98.6℉}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean body temperature = 98.42℉
s = sample standard deviation = 0.65℉
n = sample of healthy adults = 93
So, the test statistics = [tex]\frac{98.42-98.6}{\frac{0.65}{\sqrt{93} } }[/tex] ~ [tex]t_9_2[/tex]
= -2.671
The value of t test statistics is -2.671.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -1.664 at 92 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of t as -2.671 < -1.664, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean body temperature of all healthy adults is actually less than 98.6℉.
