Hypothesis, Critical Value, Test Statistic, Equation, Sample

The manager of a driving school claims that the mean time taken to learn how to drive a car is 8 hours or less for all new drivers. A sample of 16 new drivers showed that the mean time taken by them to learn how to drive the car is 9.5 hours with a standard deviation of 1.5 hours. Test the manager's claim at the 1% significance level
a.Select the null and alternate hypothesis
b.Determine the critical values of the test statistic
c.Which equation listed below would you use?
d.Using the statistical calculator or manual calculation what is the observed statistic and what is your decision regarding the null hypothesis. Provide a one sentence answer

2. A department store manager claims that at least 45% of persons who visited this store make a purchase. In a sample of 400 persons who visited the store 150 made a purchase. Test the manager's claim at the 3% significance level
a.State the null and alternate hypothesis
b.Determine the rejection region for the decision rule
c.Which equation listed below would you use?
d.Using the statistical calculator or manual calculation what is the observed statistic and what is your decision regarding the null hypothesis. Provide a one sentence answer.

3.Complete the ANOVA summary table shown here ... (see attached file).

You have collected the following data from two suppliers. Are the suppliers significantly different at the 0.05 level of significance?
Supplier One Supplier Two
Sample Size 45 52
Sample mean 8.1 9.3
Sa

Please explain and resolve the attached problem. Thanks!
Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is = 0. Compute the value of the t test statistic.
x 7 2 7 3 10
y 4 4 3 4 5
Use three decimal places

Please help answer the following questions involving statistics.
1. Why do we use hypothesis testing?
2. What is a test statistic and how is it related to a critical value in hypothesis testing?
3. What is the critical region in hypothesis testing and why is it important?

The following hypotheses are given:
H0: π 0.70
H1: π >0.70
A sample of 100 observations revealed that p = 0.75.
At the .05 significance level, can the null hypothesis be rejected?
1. State the decision rule.
2. Compute the value of the test statistic.
3. What is your decision regarding the null hypothesis?

You will be asked to determine the correct decision (Reject Ho or Fail to Reject Ho) for each of the following tests of hypotheses.
1. A hypothesis test at the 0.025 level of significance with a p-value for the sample of 0.0075.
2. A hypothesis test at the 0.01 level of significance with a p-value for the sample of 0.012

What is the purpose of a hypothesis test? What goes in the null hypothesis and what goes in the alternate hypothesis? Why is it inappropriate to put a sample statistic in the hypothesis?
If you are testing the hypothesis
H0: population proportion is .5
H1: population proportion is not .5,
and you get .52 for the sample

Consider the following hypothesis test:
HO: µ ≥ 80
Ha: µ < 80
A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use a = .01.
a) x = 78.5
b) x = 77
c) x = 75.5
d) x = 81

A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
4.85 4.80 4.89 4.82 4.94 4.96 4.96 4.83 4.80 4.84 4.95 4.88
Assuming that = 0.10, test the hypothesis that the population mean is equal to 5.
· State the null and alternate hypothe

Consider the following hypothesis test:
Ho (null hypothesis): µ = 15
Ha (alternative hypothesis): µ ≠ 15
A sample of 25 gives a sample mean of 14.2 and sample standard deviation of 5. Answer the following questions regarding the hypothesis test.
a) At α = 0.05, what is the rejection rule?
b) Compute the value of

I am looking to understand the formula for calculating the standard deviation for the T Statistic - in the problem attached among learning th T Statistic.