How to find and calculate the info below

Question

It is believed that the mean flight time from Seattle to New York City is 310 minutes. You want to test to determine if it is different from this. The population standard deviation is 10 minutes. You randomly sample 50 flights and the sample average is 313 minutes. State your hypotheses and level of significance, calculate and state the test statistic, calculate and state the p-value, state whether you reject the Ho or fail to reject the Ho, and state your final conclusion (i.e. sufficient or insufficient evidence ...).  

Answer 1

√I am willing to take a crack at this!

Step 1. Determine the Type of Question

Since they are asking us to test if the population mean is different based on the one derived from the sample, this is a Hypothesis test question that will involve p values, Z critical values and Z test values.

Since no alpha threshold was specified, we assume a=.05

That Gives as a Z Critical Value= ± 1.96 (Derived from Statistical Appendix Tables.). It is plus or minus because we assume a two-sided test if no test is specified.

H0= µ=310 or Xbar= µ, We do not have enough evidence to suggest that the Sample mean is statistically different from the population mean.

Ha= µ≠310 or Xbar≠µ, We have evidence to suggest that the Sample mean is statistically different from the population mean.

Decision rule, if the Z Test value is outside the bounds P( -1.96 < ZTest< +1.96), then we have evidence to reject the null hypothesis.

Step2. Note your Givens

1. μ=310 (Population mean)
2. Xbar=313 (Sample Mean
3. σ=10 (Population STD)
4. n=50

Step3: Determine your Z test value

Using the formula

Ztest= (Xbar - µ) ÷ σ/√n

We get

(313 - 310) ÷ 10/√50 = 2.121 = Ztest value

Step 4. Compare Z test with Z crit.

Z Test = + 2.121

Z Crit =±1.96

P( -1.96 < 2.121< +1.96)

2.121 Lies outside the bounds of ± 1.96.

Conclusion: We have sufficient evidence to suggest that the Population mean flight time is significantly different from 310.

We reject the null hypothesis in favor of the Alternate.