In order to conduct a hypothesis test for the population mean, a random sample of 8 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 7.5 and 1.8, respectively.(You may find it useful to reference the appropriate table:z tableort table).

H₀: 6.8againstH_A:> 6.8

a-1.Calculate the value of the test statistic.(Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test Statistic

a-2.Find thep-value.

• 0.01 p-value < 0.025
• p-value < 0.01
• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

a-3.At the 1% significance level, what is the conclusion?

• Do not rejectH₀since thep-value is greater than significance level.
• Do not rejectH₀since thep-value is less than significance level.
• RejectH₀since thep-value is greater than significance level.
• RejectH₀since thep-value is less than significance level.

a-4.Interpret the results at= 0.01.

• We cannot conclude that the population mean is greater than 6.8.
• We conclude that the population mean is greater than 6.8.
• We cannot conclude that the population mean differs from 6.8.
• We conclude that the population mean differs from 6.8..

H₀:= 6.8againstH_A: 6.8

b-1.Calculate the value of the test statistic.(Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test Statistic

b-2.Find thep-value.

• 0.05 p-value < 0.10
• p-value 0.10
• 0.01 p-value < 0.025
• 0.025 p-value < 0.05
• p-value < 0.01

b-3.At the 1% significance level, what is the conclusion?

• RejectH₀since thep-value is less than significance level.
• RejectH₀since thep-value is greater than significance level.
• Do not rejectH₀since thep-value is less than significance level.
• Do not rejectH₀since thep-value is greater than significance level.

b-4.Interpret the results at= 0.01.

• We conclude that the population mean is greater than 6.8.
• We cannot conclude that the population mean is greater than 6.8.
• We conclude that the population mean differs from 6.8.
• We cannot conclude that the population mean differs from 6.8.