Question

test the claim about the population mean, u, at thegiven level of significance, a, using the given sample statistics. Assume thepopulation is normally distributed.Use the claim below to (a) identify the null and alternative hypothesis(B) identify the standardized test statistic (c) identify the P-value(D) decide whether to reject or fail to reject the null hypothesisClaim: u>1290; a=0.06; o=197.95 sample statistics X=1319.39,n=275

Answer 1

Here is the information that we have:

`\begin{gathered} Claim: \\ \mu>1290 \\ \alpha=0.06 \\ \sigma=197.95 \\ Sample\text{ Statistics:} \\ X=1319.39 \\ n=275 \end{gathered}`

A)

According to the claim and the sample statistics, the null hypothesis and the alterative hypothesis are given by:

`\begin{gathered} H_0:\mu>1290 \\ H_a:\mu\leq1290 \end{gathered}`

B)

The standardized test statistic is given by:

`|z|=|(\mu-X)/((\sigma)/(√(n)))|=|(1290-1319.39)/((197.95)/(√(275)))|=2.46`

C)

The p-value represent the probability of obtaining a result that confronts the claim. According to a normal table, for z = -2.46, the p-value is given by p = 1 - 0.5 - 0.4931 = 0.0069

D)

Since p = 0.0069 < a = 0.06, the null hypothesis is not rejected.