Answer to Question #165188 in Statistics and Probability for Bella

Question

A manufacturer of electric bulbs claims that his bulbs have a mean life of 25 months with a standard deviation of 5 months. A random sample of 6 such bulbs were taken and their lifespan were recorded.

Life of​ bulbs(in months):23 25 30 20 20 12

Is the​ manufacturer's claim valid at​ 1% level of significance when the table value of t test is​ ±4.032?

​(a) Formulate a null and alternative hypothesis.

​(b) Calculate the​ mean, standard​ deviation, and the tSTAT.

​(c) Interpret the​ manufacturer's claim.

I answered a and b but c made me confused. can anyone help me?

the choices ;

A.

The null hypothesis is rejected as tSTAT is less than the table value. Hence the​ manufacturer's claim is not valid at​ 1% level of significance.

B.

The null hypothesis is not rejected as tSTAT is more than the table value. Hence the​ manufacturer's claim is valid at​ 1% level of significance.

C.

The null hypothesis is not rejected as tSTAT is less than the table value. Hence the​ manufacturer's claim is valid at​ 1% level of significance.

D.

The null hypothesis is rejected as tSTAT is more than the table value. Hence the​ manufacturer's claim is not valid at​ 1% level of significance.

Answer 1

Solution

a).

$$H_0 : \mu =25 \space vs \space H_1 : \mu \not= 25$$

b). Mean, $\bar{x}$

$$\bar{x} ={23+25+30+20+20+12 \over 6}$$

$\bar {x} =21.6667$

Standard deviation, $S$

$$S= \sqrt {\sum (x- \bar{x}) ^2 \over n-1}$$

$$=\sqrt {181.33333 \over 5} =6.02218$$

tSTAT

$$tSTAT= {\bar{x} - \mu \over {\sigma \over \sqrt {n}}} ={21.66667 - 25 \over {5 \over \sqrt {6}}}$$ $$=-1.63299$$

c). Conclusion :

The null hypothesis is not rejected as tSTAT is less than the table value. Hence the​ manufacturer's claim is valid at​ 1% level of significance