the null hypothesis is 𝜇=90 and the alternative hypothesis is 𝜇>90 using 𝛼=.05, find the following: (a) Test statistic: (b) P - value:

Question

A random sample of 100 observations from a population with standard deviation 10.26 yielded a sample mean of 91.8.

the null hypothesis is 𝜇=90 and the alternative hypothesis is 𝜇>90  using 𝛼=.05, find the following:

(a) Test statistic:

(b) P - value:

Answer 1

You know the standard deviation of the population and you are taking a sample greater than 30, so you can assume normal distribution of the sample --> z statistic.

You know that x avg = 91.8, you assume a mu of 90, you use a standard deviation for the sample of 10.26/10

You can look up in a table or use technology to find the probability of z > (x_avg-μ)/σ_x . This will be the p value. If p < α, you reject the null hypothesis.