Question

The Moving Company claims that a typical family moves an average of once every 5.2 years. Somebody believes that this mean time between moves is longer. Random sample of 100 families showed that the mean time between moves was 5.7 years with standard deviation 1.8 years. Test the claim that the mean time is longer that 5.2 years. Use significance level α = 0.05

Answer 1

Solution :

Given that,

Population mean = = 5.2

Sample mean = = 5.7

Sample standard deviation = s = 1.8

Sample size = n = 100

Level of significance = = 0.05

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: 5.2

Ha: 5.2

The test statistics,

t = ( - )/ (s/)

= ( 5.7 - 5.2 ) / ( 1.8 / 100)

= 2.778

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.66

Since it is observed that t = 2.778 > = 1.66 it is then concluded that the null hypothesis is rejected.

P- Value = 0.0033

Using the P-value approach: The p-value is p = 0.0033 < 0.05 it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 5.2, at the 0.05 significance level.