Register

GO Classes DPP | STATISTICS |HYPOTHESIS TESTING

215 views
0 0 votes

A manufacturer claims that the average lifetime of its LED bulbs is $\mathbf{1000}$ hours.
A consumer agency randomly tests $\mathbf{50}$ bulbs and finds their mean lifetime $=\mathbf{980}$ hours with a population standard deviation $= \mathbf{60}$ hours.

At $\mathbf{5 \%}$ significance level, test whether the manufacturer's claim is valid.
 

\[
\begin{array}{|c|c|c|}
\hline
\textbf{Z-value} & \textbf{Cumulative area} & \textbf{Tail area (two-tail)} \\
\hline
1.645 & 0.950 & 0.10 \\
\hline
1.96 & 0.975 & 0.05 \\
\hline
2.33 & 0.990 & 0.02 \\
\hline
\end{array}
\]
 

  1. $\mathrm{Z}=-1.67$, Do not reject $H_0$
     
  2. $\mathrm{Z}=-2.36$, Reject $H_0$
     
  3. $\mathrm{Z}=-3.24$, Reject $H_0$
     
  4. $\mathrm{Z}=-1.12$, Do not reject $H_0$

 

1 Answer

0 0 votes

$$
\begin{aligned}
& \mu=1000 \\
& \bar{x}=980 \\
& \sigma=60 \\
& n=50 \\
& \alpha=0.05
\end{aligned}
$$


Formula:

$$
Z=\frac{\bar{X}-\mu}{\sigma / \sqrt{n}}
$$


Substitute:

$$
Z=\frac{980-1000}{60 / \sqrt{50}}=\frac{-20}{60 / 7.071}=\frac{-20}{8.485}=-2.36
$$


Critical value (two-tailed, $\alpha=0.05$ ): $\pm 1.96$


Decision: $$
|\mathrm{Z}|=2.36>1.96 \rightarrow \textbf { Reject } \mathbf{H_0}
$$

Voting & Accepting an answer helps improve the community
Answer:
← Previous · GO Classes DPP | TOC...Next → · GO Classes DPP | STA...
← Previous in category · ###Next in category → · GO Classes DPP | STA...
Position:
Show:

Related questions

0 0 votes
1 1 answer
235
235 views
GO Classes asked Nov 18, 2025
235 views
GO Classes DPP | STATISTICS |HYPOTHESIS TESTING
A dietitian claims that a new diet plan reduces average weight by $\mathbf{5~kg}$ in a month.A random sample of $\mathbf{9}$ individuals on this diet shows a mean reducti...
1 1 vote
1 1 answer
297
297 views
GO Classes asked Nov 18, 2025
297 views
GO Classes DPP | STATISTICS |EXPECTATION
A shopkeeper sells an item for ₹$100$. The probability that a customer buys the item on any given day is $0.3$. If a customer buys it, the profit is ₹$20$; otherwise, the...
0 0 votes
1 1 answer
257
257 views
GO Classes asked Nov 18, 2025
257 views
GO Classes DPP | STATISTICS |COVARIANCE
The joint distribution of two discrete random variables $X$ and $Y$ is given as follows:\[\begin{array}{|c|c|c|}\hlineX & Y & P(X, Y) \\\hline0 & 0 & 0.2 \\\hline0 & 1 & ...
0 0 votes
1 1 answer
269
269 views
GO Classes asked Nov 18, 2025
269 views
GO Classes DPP | STATISTICS |VARIANCE
The probability distribution of a discrete random variable $X$ is given by\[\begin{array}{c|cccc}X & 0 & 1 & 2 & 3 \\\hlineP(X) & 0.1 & 0.3 & 0.4 & 0.2\end{array}\] Find ...