Use the following question to answer Parts $1-4$

A manufacturer claims that the mean lifetime of florescent bulbs is $950$ hours. A homeowner selects $40$ bulbs and finds the mean lifetime to be $940$ hours with standard deviation of $80$ hours. Test the manufacturer's claim. Use $=0\mathrm{.}05.$

Step I Hypothesis

Ho: $=950($claim$)$

$$: $<mn\; id="EditorElement\_2315752">9</mn><mn\; id="EditorElement\_2315753">5</mn><mn\; id="EditorElement\_2315754">0</mn>$

Ho: $=950($claim$)$

$$: $>950$

$$: $=950$

$$: $<mn\; id="EditorElement\_2315648">9</mn><mn\; id="EditorElement\_2315649">5</mn><mn\; id="EditorElement\_2315650">0</mn><mtext\; id="EditorElement\_2315628"></mtext><mi\; id="EditorElement\_2315629">(</mi>$claim$)$

Ho: $=950($claim$)$

$$: $950$

Part $2$

Step II: Calculate the value for the Test Statistics

$-0\mathrm{.}79$

$0\mathrm{.}39$

$0\mathrm{.}13$

$-0\mathrm{.}75$

Step III Find the critical value$($s$)$ to the rejection region

Part $3$

$+-2\mathrm{.}575$

$+-1\mathrm{.}645$

$+-1\mathrm{.}96$

$+-1\mathrm{.}80$

Fill in the blanks:

Step IV: Conclusion

Part $4$

At $1\%$ level of the significance,

we $,H_0.$

There enough evidence to support the claim.

reject, is

fail to reject, is

fail to reject, is not

reject, is not