An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 3333 type K batteries and a sample of 3131 type Q batteries. The type K batteries have a mean voltage of 8.728.72, and the population standard deviation is known to be 0.4020.402. The type Q batteries have a mean voltage of 8.888.88, and the population standard deviation is known to be 0.2450.245. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1μ1 be the true mean voltage for type K batteries and μ2μ2 be the true mean voltage for type Q batteries. Use a 0.050.05 level of significance.
Step 1 of 5 :
State the null and alternative hypotheses for the test.
Step 2 of 5 : compute the value of the test statistic. Round to two decimal places.
Step 3 of 5 : Find the p value associated with the test statistic. Round to four decimal places
step 4 of 5: Decide if we reject or fail they hypothesis
Step 5 of 5: State the conclusion of the hypothesis. ( Is there sufficient evidence to support the claim)
1)
Let μ1 be the true mean voltage for type K batteries
μ2 be the true mean voltage for type Q batteries.
Use a 0.05 level of significance.
Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different.
Ho:- μ1 - μ2 = 0 vs Ha:- μ1 - μ2 ≠ 0
2)
The value of the test statistic.
x1:- voltage for type K batteries
x2:-voltage for type Q batteries.
3) p value = P( |Z| > |z|)
= 2 * P( Z > 1.94)
= 2*(1-P(Z<1.94) )
= 2* ( 1- 0.9735)
= 2* 0.0265
= 0.0529
P-value = 0.0529
4) we reject Ho when P-value < level of significance
Here P-value =0.0529 > level of significance = 0.05
we fail to reject Ho at % 5 l.o.s
5) conclusion:-
we may conclude that the data does not provide sufficient evidence to support the claim that the mean voltage for two types of batteries is different.
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