Question

1. It is claimed that the proportion of male golfers is more than 0.4 (40%).

1. State the null and alternate hypothesis that would be used to check this claim

2. Suppose a sample is taken and the requirements are met. The results of the analysis say reject the hypothesis at the 5% level of significance. Write the interpretation of this hypothesis test.

      

Answer 1

Here in this Question the they claimed that the proportion of male golfers is more than 40% (0.4) .

Then the appropriate hypothesis is given below,

Hypothesis is the tentative statement about the population.

Null hypothesis: the null hypothesis has generally no difference. According to R.A Fisher the null hypothesis is the hypothesis that tested for its possible rejection.

a) Hypothesis :  

Ho : P >=0.4 (40%) vs Ha : P < 0.4 (40%)

From the above hypothesis it clear that the test is one sided test.

b) test Statistic:

Now suppose the sample is taken and requirements are met. Before that we have to check some assumptions.

If the sample is<30 then we can use t Statistic ( t test ) and if we have sample >30 then we have to Use standard normal distribution.

2. Assumptions :We have two cases:
Case1: Population is normally or approximately
normally distributed with known or unknown
variance (sample size n may be small or large),
Case 2: Population is not normal with known or
unknown variance (n is large i.e. n≥30).

Now,

A statistical test uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected. The numerical value obtained from a statistical test is called the test value.
You will notice that our statistical tests will resemble the general formula for a z-score:
Test Value = observed value – expected value/standard error

The z test is a statistical test for the mean of a population. It can
be used when n ≥ 30, or when the population is normally
distributed and σ is known.
The formula for the z-test is:
Z= Xbar - mu /sigm/√n

Now compute the p value ( p value is the probability value of test Statistic)

Now hereCritical Value (CV) – separates the critical region from the Non-critical region, i.e., when we should reject H0 from When we should not reject H0.

Significance level - is the maximum probability of committing a Type I error. This probability is symbolized by
alpha.
P(Type I error|H0
is true) alpha

Decision rule : If p value< alpha then we reject null Ho hypothesis.

And conclude that the proportion of male golfers is less than 0.4 (40%).

This is the interpretation of given hypothesis.

Hope you understood then RATE POSITIVE ?.in case of any queries please feel free to ask in comment box. Thank you.