Question

Consider the following hypotheses:

H₀: μ = 19
H_A: μ ≠ 19

The population is normally distributed. A sample produces the following observations: (You may find it useful to reference the appropriate table: z table or t table)

20	23	17	21	21	24	23

Click here for the Excel Data File
  

a. Find the mean and the standard deviation. (Round your answers to 2 decimal places.)

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c. Find the p-value.

• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10

d. At the 5% significance level, what is the conclusion?

• Do not reject H₀ since the p-value is smaller than α.

• Do not reject H₀ since the p-value is greater than α.

• Reject H₀ since the p-value is smaller than α.

• Reject H₀ since the p-value is greater than α.

e.  Interpret the results αα = 0.05.

• We cannot conclude that the sample mean differs from 19.

• We conclude that the population mean differs from 19.

• We cannot conclude that the population mean differs from 19.

• We conclude that the sample mean differs from 19.

Answer 1

= 19 null hypothesis: Ho: Alternate Hypothesis: Hau 0.01 level with two tailed test and n-1= 6 df, critical t= 3.71 Decision rule: reject Ho if absolute value of test statistic It>3.707 21.286 population mean = sample mean x= sample size na sample std deviation s= std error sx=sh n= 2.360 0.8921 test statt='(x-u)'n's= P value 2.56 0.0428

a)mean =21.29

standard deviation =2.36

b)

value of the test statistic =2.57 (please try 2.56 if this comes wrong)

c)

0.02 p-value < 0.05

d)Reject H₀ since the p-value is smaller than α.

e)

We conclude that the sample mean differs from 19.