Dataset: 37, 25, 40, 49, 26, 33, 59, 21

μx = 51

1. What is the variance?
2. What is the mean?
3. When calculating the t-value, what is the numerator, denominator, and the final t-value?
4. Degrees of freedom
5. Critical value. Do you use one tail or two tail? Why?
6. Would you reject the null hypothesis?

Use 4 decimals for the answers.

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I did the work but not sure if my answers are correct. Please let me know if the answers are good. If your results do not coincide with mine, please let me know how you did it. Thanks so much

Mean=36.25. Sum of squares is 1169.5. Variance is 146.1875. df = 7, used two tail. t numerator is -14.75, denominator is 4.5699, t = -3.2276.

Critical value is +- 2.365

i should reject because t < -2.365

Which of the following is NOT a criterion for making a decision in a hypothesis test? Choose the correct answer below.

A.) If the test statistic falls within the critical region, the decision is to reject the null hypothesis.

B.) If a confidence interval does not include a claimed value of a population parameter, the decision is to reject the null hypothesis.

C.) If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

(1 point) A random sample of 130 observations is selected from a binomial population with unknown probability of success p. The computer value of is 0.64.

    (1) Test : : p = 0.65 against : p > 0.65. Use α= 0.05.

test statistic z =

critical z score

The final conclusion is 

⭕ A. We can reject the null hypothesis that p = 0.65 and accept that p is > 0.65.

⭕ B. There is not sufficient evidence to reject the null hypothesis that p = 0.65.

    (2) Test : p = 0.5 against :p < 0.65. Use α = 0.01.

test statistic z =

critical z score

The final conclusion is 

⭕ A. We can reject the null hypothesis that p = 0.5 and accept that p is < 0.5.

⭕ B. There is not sufficient evidence to reject the null hypothesis that p = 0.5.

   (3) Test : p = 0.55 against : p ≠ 0.55. Use α = 0.01.

test statistic z =

positive critical z score

Which of the following is NOT a criterion for making a decision in a hypothesis test?
A) If the test statistic falls within the critical region, the decision is to reject the null hypothesis.
B) If a confidence interval does not include a claimed value of a population parameter, the decision is to reject the null hypothesis.
C) If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
D) If P-value ≤ α, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.