Question

I only need answers for number 4 & 5. (Just 2 numbers)

1.) The mean instant messaging bill is P32.79 per household. A sample of 50 households showed a sample mean of P30.63. Use a population standard deviation of σ=5.60.

Formulate hypothesis for a test to determine whether the sample data support the conclusion that the mean monthly instant messaging bill is less than the national mean of P32.79.

What is the value of the test statistic?

What is the p-value?

At α=0.01, what is your conclusion?

2.) Laborers union in a protest claimed that the mean tenure for a company’s President was at least ten years. A survey of companies reported in research found a sample mean tenure of xbar=8.32 years for Presidents with a standard deviation of s=7.49 years.

Formulate hypothesis that can be used to test the validity of the claim made by the union.

Assume 90 companies were included in the sample. What is the p-value for your hypothesis test?

At α=0.01, what is your conclusion?

3.) 22% express an interest in seeing XYZ television show. KL Broadcasting Company ran commercials for this XYZ television show and conducted a survey afterwards. 1532 viewers who saw the commercials were sampled and 414 said that they would watch XYZ television show.

What is the point estimate of the proportion of the audience that said they would watch the television show after seeing the commercials?

At α=0.05, determine whether the intent to watch the television show significantly increased after seeing the television commercials. Formulate the appropriate hypothesis, compute the p-value, and state your conclusion.

4.) Create a case (please refer to #s 1-3 for sample) on the application of inferences about the difference between two population means (σ1 and σ2 known) and explain the hypothesis tests until conclusion.

5.) Create a case (please refer to #s 1-3 for sample) on the application of inferences about the difference between two population means (σ1 and σ2 unknown) and explain the hypothesis tests until conclusion.

Answer 1

1) Define the null and the laternative hypothesis as

The sample mean is 30.63 and sample size is 50, also population standard deviation is 5.60

So the value of the test statis is

Now using normal table and the fact the test is left tailed

We have P-value is

Now for 0.01 level of significance, we have P-value less than significance level, So reject the null hypothesis.

So, there is enough evidence to support the claim that mean monthly instant messaging bill is less than the national mean of 32.79

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