Question

A simple random sample of 16 adults drawn from a certain population of adults yielded a mean weight of 63kg. Assume that weights in the population are approximately normally distributed with a variance of 49. Do the sample data provide sufficient evidence for us to conclude that the mean weight for the population is less than 70 kg? Let the probability of committing a type I error be .01. 1. Write the hypotheses, indicate the claim 2. find the critical value t-value 3. calculate the standardized t -value 4. what is the decision

Answer 1

sample size , n = 16

sample mean , x_bar = 63 kg

population variance = 49 kg

SE = ( variance)^1/2 = 49^1/2 = 7 kg

H0 : Null Hypothesis : mean weight for the population 70 kg , mu = 70 kg

H1 : Alternate Hypothesis : mean weight for the population is less than 70 kg : mu < 70 kg

Level of significance : probability of committing a type I error = alpha = 0.01

Rejection Criteria : reject H0 if | t_cal | > t_critical

Degrees of freedom = n - 1 = 16 - 1 = 15

t_critical at 15 DF ( one - tailed ) = 2.602

Statistic :

t_cal = ( x_bar - mu ) / ( SE/n^1/2 ) = ( 63 - 70 )/(7/4) = - 4

| t_cal | = 4

since, | t_cal | ( 4 ) > t_critical ( 2.602 )

therefore, H0 is rejected

Or, alternate hypothesis is accepted

mean weight for the population is less than 70 kg or mu < 70 kg