The Chicago Title Insurance Company publishes statistics on

The Chicago Title Insurance Company publishes statistics on recent home buyers in the The Guarantor. According to that publication, 83.1% of home buyers in 1995 purchased single-family houses. Out of 200 randomly selected home buyers for this year, 152 purchased single-family houses. Do the data provide sufficient evidence to conclude that this year\'s percentage of home buyers purchasing single-family houses is different from the 1995 figure of 83.1%? Use a = 0.021. (Use p-value approach.)

3. The owner of an exercise club believes the mean value of the amount of weight lost in a program during six months should be at least 30 pounds. The number of pounds lost by a sample of 29 people over six months are given below:

3, 4, 5, 5, 6, 7, 7, 10, 10, 10, 12, 12, 15, 15, 18, 18, 20, 23, 24, 25, 25, 28, 29, 30, 35, 40, 41, 44, 45

Can you reject the owner

Solution

The null hypothesis is

(The percentage of population proportion is 83.1%)

Against the alternative hypothesis

(The percentage of population proportion is different from 83.1%)

Now, 152 (x) buyers purchased single family houses out of 200 (x) buyers.

Thus, calculate the sample proportion

Calculate the standard deviation

The p value corresponding the test statistic is 0.0092+0.0091=0.0182 which is less than alpha=0.021, thus reject the null hypothesis.

The null hypothesis is

(The population mean is 30 pounds)

Against the alternative hypothesis

(The population mean is different from 30 pounds)

Use in two tails.

The mean and standard deviation of 30 observations are 19.367 pounds (M) and 12.615 pounds (S).

The degrees of freedom is-

Calculate the estimated standard error-

Now, calculate the t- statistic

From t- table, we find the critical value of ,

The test statistic falls in the critical region, reject the null hypothesis at 0.01 level. Thus, it can be concluded that the tests is significant.